Isoperimetric inequalities and the gap between the first and second eigenvalues of an Euclidean domain

Shiu‐Yuen Cheng, Kevin Oden

Type: Article

Publication Date: 1997-06-01

Citations: 17

DOI: https://doi.org/10.1007/bf02921721

View Publication

Locations

Journal of Geometric Analysis - View

Similar Works

Action	Title	Year	Authors
+	Isoperimetric inequalities of Euclidean type and applications	2004	Stefan Wenger
+	Isoperimetric Inequalities for Eigenvalues and Their Applications	2011	L. E. Payne
+	Isoperimetric Inequalities and Applications.	1984	L. E. Payne Catherine Bandle
+	Isoperimetric inequalities and applications	1980	Catherine Bandle
+	Isoperimetric Inequalities and Their Applications	1967	L. E. Payne
+	Isoperimetric Inequalities and Applications	2017	Martin T. Barlow
+	The Isoperimetric Inequality and Related Inequalities	1989	Heinz Hopf
+ PDF Chat	Isoperimetric inequalities of Euclidean type in metric spaces	2005	Stefan Wenger
+	THE ISOPERIMETRIC INEQUALITY AND EIGENVALUES OF THE LAPLACIAN	1991	Themistocles M. Rassias
+	Isoperimetric inequalities and concave functions	1999	Alane Susan Ferland
+	A class of isoperimetric inequalities	1985	R. R. Hall
+	The Isoperimetric Inequality and Related Inequalities	1983	Heinz Hopf
+	Isoperimetric inequalities for eigenvalues of the Laplacian	2007	Mark S. Ashbaugh Rafael D. Benguria
+ PDF Chat	Isoperimetric inequality and spectral geometry	1996	Takashi Sakai
+ PDF Chat	Isoperimetric inequalities	2003	Katsuhiro Shiohama Takashi Shioya Minoru Tanaka
+	Isoperimetric Inequalities and Quasi-Isometries	2007
+	Isoperimetric inequalities for eigenvalues of the Laplacian	2011	Rafael D. Benguria
+	Isoperimetric upper bounds for the first eigenvalue	2012	G. Santhanam
+	Isoperimetric inequalities	1983	Catherine Bandle
+	Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces	2024	Yifeng Meng Kui Wang

Works That Cite This (15)

Action	Title	Year	Authors
+	Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs	2020	Bobo Hua Lili Wang
+ PDF Chat	An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift	2005	François Hamel Nikolaï Nadirashvili Emmanuel Russ
+ PDF Chat	Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains	2023	Xavier Ramos Olivé Christian Rose Lili Wang Guofang Wei
+	Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string	2014	Behrouz Emamizadeh Amin Farjudian
+ PDF Chat	Nash inequalities for compact manifolds with boundary	2001	Hironori Kumura
+ PDF Chat	Symmetrization of functions and principal eigenvalues of elliptic operators	2014	François Hamel Nikolaï Nadirashvili Emmanuel Russ
+	Local Sobolev constant estimate for integral Bakry–Émery Ricci curvature	2019	Lili Wang Guofang Wei
+ PDF Chat	L<sup>2</sup>ESTIMATES FOR THE EIGENFUNCTIONS CORRESPONDING TO REAL EIGENVALUES OF THE TRICOMI OPERATOR	2011	Alberto Favaron
+ PDF Chat	Weighted graph Laplacians and isoperimetric inequalities	2000	Fan Chung Kevin Oden
+ PDF Chat	Rearrangement inequalities and applications to isoperimetric problems for eigenvalues	2011	François Hamel Nikolaï Nadirashvili Emmanuel Russ

Works Cited by This (10)

Action	Title	Year	Authors
+	A Lower Bound for the Smallest Eigenvalue of the Laplacian	2015	Jeff Cheeger
+	The bottom of the spectrum of a Riemannian covering.	1985	Robert Brooks
+ PDF Chat	Isoperimetric constants and the first eigenvalue of a compact riemannian manifold	1975	Shing‐Tung Yau
+	On the Ratio of Consecutive Eigenvalues	1956	L. E. Payne Georg Pólya Hans F. Weinberger
+	On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions, and with an Application to the Diffusion Equation	2002	H. J. Brascamp Élliott H. Lieb
+	A Sharp Bound for the Ratio of the First Two Eigenvalues of Dirichlet Laplacians and Extensions	1992	Mark S. Ashbaugh Rafael D. Benguria
+	An estimate of the gap of the first two eigenvalues in the Schrödinger operator	1985	I. M. Singer Bun Wong Shing‐Tung Yau Stephen S.‐T. Yau
+	ON THE TOTAL CURVATURE OF IMMERSED MANIFOLDS	1996	Shiing-Shen Chern Richard Lashof
+	Estimates of eigenvalues of a compact Riemannian manifold	1980	Peter Li Shing Tung Yau
+	On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation	1976	H. J. Brascamp Élliott H. Lieb