Isoperimetric bounds for the first eigenvalue of the Laplacian

DOI10.1007/S00033-009-0001-7zbMath1192.35125OpenAlexW2134809841MaRDI QIDQ980687

Qiaoling Wang, Chang-Yu Xia

Publication date: 29 June 2010

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-009-0001-7

zbMATH Keywords

minimal surfaceEuclidean spacefirst eigenvalueLaplacianhypersurfacesfixed membrane problem

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Membranes (74K15)

Related Items (7)

Isoperimetric bounds for lower-order eigenvalues ⋮ Energy decay in thermoelastic diffusion theory with second sound and dissipative boundary ⋮ Two isoperimetric inequalities for the Sobolev constant ⋮ Weighted isoperimetric inequalities in warped product manifolds ⋮ A Payne-Rayner type inequality for the Robin problem on arbitrary minimal surfaces in \(\mathbb R^N\) ⋮ Unnamed Item ⋮ Isoperimetric inequalities for eigenvalues by inverse mean curvature flow

Cites Work

• Isoperimetric monotonicity and isoperimetric inequalities of Payne-Rayner type for the first eigenfunction of the Helmholtz problem
• Sur la premiere fonction propre d'une membrane: une extension à N dimensions de l'inégalité isoperimetrique de Payne-Rayner
• A reverse Hölder inequality for the eigenfunctions of linear second order elliptic operators
• A weighted isoperimetric inequality and applications to symmetrization
• An isoperimetric inequality for the first eigenfunction in the fixed membrane problem
• Some isoperimetric norm bounds for solutions of the Helmholtz equation
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