Björn Gustafsson

Björn Gustafsson

Professor emeritus in Mathematics

Address: Deparment of Mathematics, KTH, 100 44 Stockholm, Sweden.
Office: 3447, Lindstedtsvägen 25.
Fax: int + 46 8 723 1788
Email: gbjorn@kth.se

Short CV and list of publications:

CV, Publications

Books:

B. Gustafsson, Yu-Lin Lin: Laplacian growth on branched Riemann surfaces, Lecture Notes in Mathematics 2287, ISBN 978-3-030-69862-1, Springer, 2021.
Update: After the publication of the book, a major conjecture in it has been resolved by S. Gardiner and T. Sjödin (Analysis and Mathematical Physics, 2022).
B. Gustafsson, M. Putinar: Hyponormal quantization of planar domains, Lecture Notes in Mathematics 2199, ISBN 978-3-319-65809-4, Springer, 2017.
Errata to book.
B. Gustafsson, R. Teodorescu, A. Vasil'ev: Classical and Stochastic Laplacian Growth, ISBN 978-3-319-08286-8, Springer/Birkhäuser Verlag, 2014.
B. Gustafsson, A. Vasil'ev: Conformal and Potential Analysis in Hele-Shaw Cells, ISBN 3-7643-7703-8, Birkhäuser Verlag, 2006.
Errata to book.

Editorial:

Analysis and Mathematical Physics, ISSN 1664-2368 (associate editor 2011-2020).
B. Gustafsson, A. Vasil'ev (editors): Analysis and Mathematical Physics, ISBN 978-3-7643-9905-4, Birkhäuser Verlag, 2009.
P. Ebenfelt, B. Gustafsson, D. Khavinson, M. Putinar (editors): Quadrature Domains and Applications -- a Harold S.Shapiro Anniversary Volume, Operator Theory: Advances and Applications, Vol 156, ISBN 978-3-7643-7145-6, Birkhäuser Verlag, 2005.

Papers available as pdf-files:

B. Gustafsson: Quadrature for quadrics, arXiv:2302.13882 [math.CV] PDF.
B. Gustafsson: Vortex pairs and dipoles on closed surfaces,
Journal of Nonlinear Science (2022) 32:62. PDF.
See also arXiv:2201.00528 [math-ph] PDF.
S. Bell, B. Gustafsson: Ruminations on Hejhal's theorem about the Bergman and Szegö kernels,
arXiv:1902.00959 [math.SP] PDF and Analysis and Mathematical Physics, 2022.
B. Gustafsson, A. Sebbar: Hadamard's variational formula in terms of stress and strain tensors,
Analysis and Mathematical Physics, 2022. PDF.
See also arXiv:2006.10360 [math.SP]: Hadamard's variational formula and the energy-momentum tensor, PDF
B. Gustafsson, M. Putinar: Finite term relations for the exponential orthogonal polynomials,
arXiv:1902.00959 [math.SP] PDF and Mathematical Modelling of Natural Phenomena 15 (2020) 5, DOI.org/10.1051/mmnp/2019025.
B. Gustafsson: Vortex motion and geometric function theory: the role of connections,
arXiv:1811.09430 [math-ph] PDF and Philosophical Transactions of the Royal Society A 377 (2019), DOI 10.1098/rsta.2018.0341.
B. Gustafsson, M. Putinar: A field theoretic operator model and Cowen-Douglas class,
arXiv:1810.12409 [math.FA] PDF and Banach J. Math. Anal. 13 (2019), 338--358.
B. Gustafsson: The string equation for non-univalent functions,
arXiv:1803.03020 [math.CV] PDF. Published as two articles:
1) The string equation for polynomials, Anal. Math. Phys. 8 (2018), 637--653, DOI 10.1007/s13324-018-0239-3.
2) The string equation for some rational functions, p. 213--235 in Analysis as a Life, Trends in Mathematics, Springer Nature, Switzerland 2019.
B. Gustafsson, M. Putinar: Line bundles defined by the Schwarz function,
arXiv:1711.03281 [math.CV] PDF and Anal. Math. Phys. 8 (2018), 171--183.
B. Gustafsson, J. Roos: Partial balayage on Riemannian manifolds,
arXiv:1605.03102 [math.DG] PDF and J. Math. Pures Appl. 118 (2018), 82--127.
B. Gustafsson: Laplacian growth on a branched Riemann surface, PDF,
p. 145--161 in "Analysis on Shapes of Solutions to Partial Differential Equations", RIMS, Kokyuroku No. 2082, 2018.
B. Gustafsson, Yu-Lin Lin: Non-univalent solutions of the Polubarinova-Galin equation,
arXiv:1411.1909 [math.CV] PDF, preprint 2014. (Updated version: PDF)
B. Gustafsson: Exponential transforms, resultants and moments,
arXiv:1212.0678 [math.CV] PDF and p.287--323 in Harmonic and Complex Analysis and its Applications (ed. A. Vasil'ev), Birkhäuser, 2014.
B. Gustafsson, Yu-Lin Lin: On the dynamics of roots and poles for solutions of the Polubarinova-Galin equation,
arXiv:1112.0133 [math.CV] PDF and Ann. Acad. Sci. Fenn. Math. 38 (2013), 259--286.
B. Gustafsson, M. Sakai: On the curvature of some free boundaries in higher dimensions,
arXiv:1112.4673 [math.AP] PDF and Anal. Math. Phys. 2 (2012), 247--275.
B. Gustafsson, A. Sebbar: Critical points of Green's function and geometric function theory,
arXiv:math.CV/0912.1223 (2009) PDF. A slightly shorter version in Indiana Univ. Math. J. 61 (2012), 939--1017.
B. Gustafsson, V. Tkachev: On the exponential transform of multi-sheeted algebraic domains,
arXiv:1101.0799 [math.CV]. PDF and Computational Methods and Function Theory 11 (2011), 591--615.
B. Gustafsson, V. Tkachev: On the exponential transform of lemniscates,
arXiv:1101.0794 [math.CV] PDF and p. 239--257 in Notions of Positivity and the Geometry of Polynomials,
Trends in Mathematics, 2011 (eds. P. Bränden, M. Passare, M. Putinar).
S. Bell, B. Gustafsson, Z. Sylvan: Szegö coordinates, quadrature domains, and double quadrature domains,
arXiv:math.CV/1003.2195 (2010) PDF and Computational Methods and Function Theory 11 (2011), 25--44.
B. Gustafsson, V. Tkachev: On the Jacobian of the harmonic moment map,
arXiv:math.CV/0903.3471 and Complex Analysis and Operator Theory 3 (2009), 399--417. PDF
B. Gustafsson, M. Putinar, E.B. Saff, N. Stylianopoulos: Bergman polynomials on an archipelago: estimates, zeros and shape reconstruction,
arXiv:math.CV/0811.1715 and Adv. Math. 222 (2009), 1405--1460. PDF
B. Gustafsson, M. Putinar, E.B. Saff, N. Stylianopoulos: Les polynomes orthogonaux de Bergman sur un archipel,
C.R. Math. Acad. Sci. Paris, 346 (2008), no.9-10, 499--502. PDF
B. Gustafsson, V. Tkachev: The resultant on compact Riemann surfaces,
arXiv:math.CV/0710.2326 and Comm. Math. Phys. 286 (2009), 313-358. PDF
B. Gustafsson, J. Mossino: A criterion for H-convergence in linear elasticity, Asymptotic Analysis, 51 (2007), 247-269. PDF
B. Gustafsson, M. Putinar: Selected topics on quadrature domains,
Physica D 235 (2007), 90-100. PDF
B. Gustafsson, M. Putinar: Analytic continuation of the exponential transform from convex cavities,
J. Math. Anal. Appl. 328 (2007), 995-1006. PDF
B. Gustafsson, J. Mossino: A note on H-convergence. arXiv:math.AP/0608286. PDF
B. Gustafsson, J. Mossino: Compensated compactness for homogenization and reduction of dimension: the case of elastic laminates,
Asymptotic Analysis, 47 (2006), 139-169. PDF
B. Gustafsson, H. S. Shapiro: What is a quadrature domain? p.1-25 in
P.Ebenfelt, B.Gustafsson, D.Khavinson, M.Putinar (editors), Quadrature Domains and Applications -- a Harold S.Shapiro Anniversary Volume,
Operator Theory: Advances and Applications, Vol 156, ISBN 3-7643-7145-5, Birkhäuser Verlag, 2005. PDF
B. Gustafsson, A. Vasil'ev: Nonbranching weak and starshaped strong solutions for Hele-Shaw dynamics,
Arch. Math. 84 (2005), 551-558. PDF
B. Gustafsson, M. Putinar: Linear analysis of quadrature domains IV, p.173-194 in
P.Ebenfelt, B.Gustafsson, D.Khavinson, M.Putinar (editors), Quadrature Domains and Applications -- a Harold S.Shapiro Anniversary Volume,
Operator Theory: Advances and Applications, Vol 156, ISBN 3-7643-7145-5, Birkhäuser Verlag, 2005. PDF
B. Gustafsson: Lectures on Balayage,
p. 17--63 in Clifford Algebras and Potential Theory, proceedings of the summer school held in Mekrijärvi, June 24-- 28, 2002.
University of Joensuu Department of Mathematics, Report series no. 7, ed., Sirkka-Liisa Eriksson. PDF
B. Gustafsson, D. Prokhorov, A. Vasil'ev: Infinite lifetime for starlike dynamics in Hele-Shaw cells,
Proc. Amer. Math. Soc., 132 (2004), 2661-2669. PDF
B. Gustafsson, M. Sakai: On the curvature of the free boundary for the obstacle problem in two dimensions,
Monatshefte für Mathematik 142 (2004), 1-5. PDF
B. Gustafsson, M. Sakai: Sharp estimates of the curvature of some free boundaries in two dimension
Ann. Acad. Sci. Fenn. Math. 28 (2003), 123-142. PDF
B. Gustafsson, M. Putinar: The exponential transform: a renormalized Riesz potential at critical exponent
Indiana Univ. Math. J. 52 (2003), 527-568. PDF
B. Gustafsson, M. Putinar, H. S. Shapiro: Restriction operators, balayage and doubly orthogonal systems of analytic functions
J. Funct. Anal. 199(2003), 332-378. PDF
B. Gustafsson, J. Mossino: Nonperiodic explicit homogenization and reduction of dimension: the linear case
IMA J. Appl. Math. 68 (2003), 269-298. PDF
B. Gustafsson, J. Mossino: Explicit limits for nonperiodic homogenization and reduction of dimension,
C.R. Math. Acad. Sci. Paris 334 (2002), 977--982. PDF
A. Gaudiello, B. Gustafsson, C. Lefter, J. Mossino: Asymptotic analysis of a class of minimization problems in a thin multidomain,
Calculus of Variations and Partial differential Equations, 15 (2002), 181--201. PDF
A. Gaudiello, B. Gustafsson, C. Lefter, J. Mossino: Asymptotic analysis for monotone quasilinear problems in a thin multidomain,
Differential and Integral Equations 15(2002), 623--640. PDF.
B. Gustafsson, M. Putinar: Analytic continuation of Cauchy and exponential transforms,
p. 47--57 in Analytic extension formulas and their applications (Fukuoka, 1999/Kyoto, 2000), Int. Soc. Anal. Appl. Comput., 9,
Kluwer Acad. Publ. Dordrecht, 2001. PDF (preprint version).
B. Gustafsson, B. Heron, J. Mossino: Gamma-convergence of stratified media with measure valued limits,
Asymptotic Analysis 22 (2000), 261-302. PDF
A. Gaudiello, B. Gustafsson, C. Lefter, J. Mossino: Coupled and uncoupled limits for a N-dimensional multidomain Neumann problem,
C.R. Acad. Sci. Paris, 330, Sèrie I, (2000), 985--990. PDF
B. Gustafsson, C. He, P. Milanfar, M. Putinar: Reconstructing planar domains from their moments,
Inverse Problems 16 (2000), 1053--1070. PDF
G. Golub, B. Gustafsson, P. Milanfar, P. Putinar, J. Varah: Shape reconstruction from moments: theory, algorithms, and applications, SPIE Proceedings vol. 4116 (2000),
Advanced Signal Processing, Algorithms, Architecture, and Implementations X (Franklin T.~Luk, ed.) pp. 406--416. PDF
B. Gustafsson, M. Putinar: Linear analysis of quadrature domains II,
Israel J. Math. 119 (2000), 187--216. PDF
B. Gustafsson, M. Putinar: On exact quadrature formulas for harmonic functions on polyhedra,
Proc. Amer. Math. Soc. 128 (2000), 1427--1432. PDF
B. Gustafsson, M. Sakai: On potential theoretic skeletons of polyhedra,
Geom. Dedicata 76 (1999), 1--30. PDF
B. Gustafsson: On mother bodies of convex polyhedra,
SIAM J. Math. Anal. 29:5 (1998), 1106--1117. PDF
B. Gustafsson, M. Putinar: An exponential transform and regularity of free boundaries in two dimensions,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)26 (1998), 507--543. PDF
B. Gustafsson: Direct and inverse balayage --- some new developments in classical potential theory,
in Proceedings of the Second World congress of Nonlinear Analysts, Nonlinear Anal. 30:5 (1997), 2557--2565. PDF
B. Gustafsson, M. Sakai, H. S. Shapiro: On domains in which harmonic functions satisfy generalized mean-value properties,
Potential Anal. 7 (1997), 467--484. PDF
M. Flucher, B. Gustafsson: Vortex motion in two-dimensional hydromechanics (TRITA-MAT-1997-MA-02). PDF
(Partly published as Ch.15 in M. Flucher: Variational Problems with Concentration, Birkhäuser, 1999.)
B. Gustafsson, B. Heron, J. Mossino: Gamma-comvergence relaxee et application a des problemes non coercifs,
C.R. Acad. Sci. Paris, Ser. I Math 323 (1996), 7-12. Preprint version: PDF
B. Gustafsson, H. Shahgholian: Existence and geometric properties of solutions of a free boundary problem in potential theory,
J. reine angew. Math. 473 (1996), 137--179. PDF
B. Gustafsson: A distortion theorem for quadrature domains for harmonic functions,
J. Math. Anal. Appl. 202 (1996), 169--182. PDF
B. Gustafsson, D. Khavinson: On annihilators of harmonic vector fields,
Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POM) 232 (1996), Issled. po Linein. Oper. i Teor. Funktsii. 24, 90--108, 215. PDF
B. Gustafsson, M. Sakai: Properties of some balayage operators with applications to quadrature domains and moving boundary problems,
Nonlinear Anal. 22 (1994), 1221--1245. PDF
B. Gustafsson, D. Khavinson: On approximation by harmonic fields,
Houston J. Math. 20 (1994), 75--92. PDF
B. Gustafsson, J. Mossino, C. Picard: H-convergence for stratified structures with high conductivity,
Adv. Math. Sci.Appl. 4 (1994), 265--284. PDF
B. Gustafsson, J. Mossino, C. Picard: Stratified material allowing asymptotically prescribed equipotentials,
Ark. Mat. 32 (1994), 293--307. PDF
B. Gustafsson, M. Sakai: Some geometric properties of solutions of a Hele-Shaw flow moving boundary problem, in
Free boundary problems in fluid flow with applications (eds. J.Mm Chadam and H. Rasmussen), pp. 53--57, Longman 1993. PDF
B. Gustafsson, J. Mossino, C. Picard: Homogenization of foliated annuli,
Ann.Mat. Pura Appl. 162 (1992), 87--104. PDF
B. Gustafsson, M. Sakai: An approximation theorem for integrable harmonic vector fields,
Math. Scand. 70 (1992), 78--90. PDF
B. Gustafsson: On quadrature domains, graviequivalence and balayage,
Contribution for conference proceedings (Sofia 1990, unpublished). PDF
B. Gustafsson: On quadrature domains and an inverse problem in potential theory,
J. Analyse Math. 55 (1990), 172--216. PDF
B. Gustafsson, J. Peetre: Hankel forms on multiply connected plane domains. Part two. The case of higher connectivity,
Complex Variables 13 (1990), 239-250. PDF
B. Gustafsson: On the convexity of a solution of Liouville's equation,
Duke Math. J. 60 (1989), 303--311. PDF
B. Gustafsson, J. Peetre: Möbius invariant (differential) operators on Riemann surfaces, in Function Spaces,
Operators and Non-Linear Analysis (ed. L. Päivärinta), pp. 14--75, Longman 1989. PDF (preprint version).
B. Gustafsson, J. Mossino: Isoperimetric inequalities for the Stefan problem,
SIAM J. Math. Anal. 20 (1989), 1095--1108. PDF
B. Gustafsson, J. Peetre: Notes on projective structures on complex manifolds,
Nagoya Math. J. 116 (1989), 63-88. PDF
B. Gustafsson: Singular and special points on quadrature domains from an algebraic geometric point of view,
J. Analyse Math. 51 (1988), 91--117. PDF
B. Gustafsson, J. Mossino: Some isoperimetric inequalities in electrochemistry and Hele Shaw flows,
IMA J. Appl. Math. 39 (1987), 33--49. PDF
B. Gustafsson: Application of half-order differentials on Riemann surfaces to quadrature identities for arc-length,
J. Analyse Math. 51 (1987), 54--89. PDF
B. Gustafsson: An ill-posed moving boundary problem for doubly-connected domains,
Ark. Mat. 25 (1987), 331--353. PDF
A. Friedman, B. Gustafsson: Identification of the conductivity coefficient in an elliptic equation,
SIAM J. Anal. 18 (1987), 777-787. PDF
B. Gustafsson: A simple proof of the regularity theorem for the variational inequality of the obstacle problem,
Nonlinear Anal. 10 (1986), 1487--1490. PDF
B. Gustafsson: Existence of weak backward solutions to a generalized Hele Shaw flow moving boundary problem,
Nonlinear Anal. 9 (1985), 203--215. PDF
B. Gustafsson: Applications of variational inequalities to a moving boundary problem for Hele Shaw flows,
SIAM J. Math. Anal. 16 (1985), 279-300. PDF
(Preprint version, TRITA-MAT-1981-9: PDF )
B. Gustafsson: On a differential equation arising in a Hele-Shaw flow moving boundary problem,
Ark. Mat. 22 (1984), 251--268. PDF (Preprint version, TRITA-MAT-1981-36, which contains an
introductory section on the derivation of the Hele-Shaw equation: PDF)
B. Gustafsson: Variational inequality formulation of a moving boundary problem in rock mechanics,
TRITA-MAT-1984-8 (unpublished research bulletin). PDF
B. Gustafsson: Quadrature identities and the Schottky double,
Acta Applicandae Mathematicae 1 (1983), 209--240. PDF
(Preprint version, TRITA-MAT-1977-3: PDF )
B. Gustafsson: Topics in geometric function theory and related questions of hydrodynamics,
TRITA-MAT-1981-22 (doctoral dissertation; a summary of TRITA-MAT-1977-3, -1979-7 and -1981-9). PDF
B. Gustafsson: On the motion of a vortex in two-dimensional flow of an ideal fluid in simply and multiply connected domains,
TRITA-MAT-1979-7 (unpublished research bulletin). PDF
B. Gustafsson: The Runge approximation theorem on compact Riemann surfaces,
TRITA-MAT-1977-2 (unpublished research bulletin). PDF

Updated March 23, 2023.