SOME ISOPERIMETRIC PROBLEMS
Vol. 22 No. 82 (1998), Mathematics
Vol. 22 No. 82 (1998)

SOME ISOPERIMETRIC PROBLEMS

Mathematics
https://doi.org/10.18257/raccefyn.22(82).1998.2879
Published 2024-08-02
José F. Escobar
Department of Mathematics, Cornell University, lthaca, NY 14853,
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How to Cite

Escobar, J. F. (2024). SOME ISOPERIMETRIC PROBLEMS. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 22(82), 109–115. https://doi.org/10.18257/raccefyn.22(82).1998.2879
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Abstract

We study the classical isoperimetric inequ~lity, eigenvalues for the Laplacian and Sobolev inequalities on curved spaces and the relationship among them.

https://doi.org/10.18257/raccefyn.22(82).1998.2879

Keywords

lsoperimetric inequalities | curved spaces
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References

Beckner, W. Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Annals of Math. No. 138, 1993, 213-242.

Burago, Y. and Zalgaller, V. Geometric Inequalities, Springer-Verlag, 1988.

Carathéodory, C. and Study, E. Zwei Beweise des Satzes, dass der Kreis unter allen Figuren gleichen Umfanges den größten Inhalt hat, Math. Ann. Vol. 58, 1910, 133-140.

Cao, J. and Escobar, J. F. An isoperimetric comparison theorem for PL-manifolds of non-positive curvature, Manuscrito.

Croke, C. A sharp four-dimensional isoperimetric inequality, Comm. Math. Helv. 59, 1984, 419-435.

Edler, F. Vervollständigung der Steinerschen elementargeometrischen Beweise für den Satz, dass der Kreis größeren Flächeninhalt besitzt als jede andere Figur gleichen Umfanges, Gott. Nachr. 1882, p. 73.

Escobar, J. F. Sharp Constant in a Sobolev Trace Inequality, Indiana Univ. Math. Journal, Vol. 37, No. 3, 1988, 687-698.

Escobar, J. F. Uniqueness theorems on conformal deformations of metrics, Sobolev inequalities and an eigenvalue estimate, Comm. on Pure and Appl. Math., Vol. 43, No. 7, 1990, 857-883.

Escobar, J. F. The Yamabe problem on manifolds with boundary, Jour. of Diff. Geom., Vol. 25, 1992, 21-84.

Escobar, J. F. Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary, Annals of Mathematics, Vol. 136, 1992, 1-50.

Escobar, J. F. Conformal deformation of a Riemannian metric to constant scalar curvature and constant mean curvature on the boundary, Indiana Univ. Math. Journal, Vol. 45, No. 4, 1996, 917-943.

Escobar, J. F. The Geometry of First Non-zero Stekloff Eigenvalue, aparecerá en Jour. of Functional Analysis.

Kleiner, B. An isoperimetric comparison theorem, Inventiones Mathematicae, Vol. 108, 1992, 37-47.

Osserman, R. The isoperimetric inequality, Bulletin of the AMS, Vol. 84, No. 6, 1978, 1181-1238.

Schmidt, E. Über das isoperimetrische Problem im Raum von n Dimensionen, Math. Z. 44, 1939, 689-788.

Schwarz, H. A. Beweise des Satzes, dass die Kugel kleinere Oberfläche besitzt, als jeder andere Körper gleichen Volumens, Gott. Nachr. 1884, pp. 1-13.

Steiner, J. Einfache Beweise der isoperimetrischen Hauptsätze, J. reine angew. Math. 18, 1838, 281-296.

Weil, A. Sur les surfaces en courbure négative, C. R. Acad. Sci., Paris 182, 1926, 1069-1071.

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