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A. Solynin, V. Zalgaller (2005)
An isoperimetric inequality for logarithmic *capacity of polygonsAnnals of Mathematics, 159
(1984)
Extremal decompositions of the plane or disk into two nonoverlapping domains
V. Dubinin (2014)
Condenser Capacities and Symmetrization in Geometric Function Theory
R. Laugesen, B. Siudeja (2010)
Dirichlet eigenvalue sums on triangles are minimal for equilateralsarXiv: Spectral Theory
(1971)
The solution of the Dirichlet problem for the equation u = −1 in a convex region
(1988)
Level lines of functions that are convex in the direction of an axis
R. Barnard, P. Hadjicostas, A. Solynin (2005)
The Poincaré metric and isoperimetric inequalities for hyperbolic polygonsTransactions of the American Mathematical Society, 357
Hans Haegi (1950)
Extremalprobleme und Ungleichungen konformer Gebietsgrössen
A. Solynin, V. Zalgaller (2010)
The inradius, the first eigenvalue, and the torsional rigidity of curvilinear polygonsBulletin of the London Mathematical Society, 42
J. Jenkins (1969)
On Certain Geometrical Problems Associated with CapacityMathematische Nachrichten, 39
H. Brascamp, E. Lieb (2002)
Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma
F. Brock (2000)
Continuous rearrangement and symmetry of solutions of elliptic problemsProceedings of the Indian Academy of Sciences - Mathematical Sciences, 110
P. Lionst (1981)
Two geometrical properties of solutions of semilinear problemsApplicable Analysis, 12
F. Hamel, N. Nadirashvili, Y. Sire (2013)
Convexity of level sets for elliptic problems in convex domains or convex rings: Two counterexamplesAmerican Journal of Mathematics, 138
B. Siudeja (2007)
Isoperimetric inequalities for eigenvalues of trianglesIndiana University Mathematics Journal, 59
(1996)
Polarization and functional inequalities
A. McNabb (1967)
Partial Steiner symmetrization and some conduction problemsJournal of Mathematical Analysis and Applications, 17
F. Brock, A. Solynin (1999)
An approach to symmetrization via polarizationTransactions of the American Mathematical Society, 352
S. Ruscheweyh, L. Salinas (1989)
On the preservation of direction-convexity and the Goodman-Saff conjecture, 14
G. Goluzin (1969)
Geometric theory of functions of a complex variable
G. Pólya, G. Szegő (1983)
Problems and theorems in analysis
J. Anderson, K. Barth, D. Brannan (2006)
Research Problems in Complex Analysis
A. Solynin (1992)
Continuous symmetrization of setsJournal of Soviet Mathematics, 59
G. Kuzʹmina (1982)
Moduli of families of curves and quadratic differentials
A. Solynin (2011)
Continuous symmetrization via polarizationarXiv: Analysis of PDEs
(2019)
II, Symmetrization in analysis. With David Drasin and Richard S. Laugesen. With a foreword by Walter Hayman
P. Freitas, B. Siudeja (2010)
Bounds for the first Dirichlet eigenvalue of triangles and quadrilateralsESAIM: Control, Optimisation and Calculus of Variations, 16
G. Pólya, G. Szegö (1976)
Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions
(2017)
Triangles and Other Special Domains. Shape Optimization and Spectral Theory
Filippo Bracci, Manuel Contreras, S. Díaz-Madrigal (2020)
Univalent FunctionsSpringer Monographs in Mathematics
F. Brock (1995)
Continuous Steiner‐SymmetrizationMathematische Nachrichten, 172
G. Pólya, G. Szegő (1951)
Isoperimetric inequalities in mathematical physics
A. Goodman, E. Saff (1979)
On univalent functions convex in one direction, 73
A. Acker, L. Payne, G. Philippin (1981)
On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problemZeitschrift für angewandte Mathematik und Physik ZAMP, 32
Matthew Fleeman, Brian Simanek (2017)
Torsional Rigidity and Bergman Analytic Content of Simply Connected RegionsComputational Methods and Function Theory, 19
(1985)
Transformation of functions and the Dirichlet principle
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In this paper, we discuss the Pólya–Szegő continuous symmetrization and its applications to isoperimetric inequalities. In particular, we survey results concerning monotonicity properties of certain characteristics, including torsional rigidity of cylindrical beams and principal frequency of a uniformly stretched elastic membrane of a drum, of triangles and other domains. Several remaining open problems on continuous symmetrization and relevant properties of domains and functions are also discussed.
Computational Methods and Function Theory – Springer Journals
Published: Nov 13, 2020
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