Isoperimetric inequalities for eigenvalues by inverse mean curvature flow

[摘要] In this paper, we consider the closed eigenvalue problem on hypersurfaces evolving under the inverse mean curvature flow (IMCF) in Rn+1, prove that the first nonzero eigenvalue of p-Laplacian (p > 1) is non-increasing along this flow, and find an interesting monotone quantity associated with the eigenvalue along the rescaled IMCF. Finally, using a new pinching condition preserved along the IMCF, the isoperimetric lower bound for this eigenvalue is determined. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Eigenvalues;Inverse mean curvature flow;Monotonicity;Inequality