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A remark on the first eigenvalue of the p-Laplacian on compact submanifolds in the unit sphere

Matheus Nunes Soares, Fábio Reis dos Santos

Abstract

An integral inequality for the singular p-laplacian is established for 3/2<p<2. As consequence, lower bounds for the first eigenvalue of the p-laplacian are obtained for minimal submanifolds and prescribed scalar curvature submanifolds in the unit sphere.

A remark on the first eigenvalue of the p-Laplacian on compact submanifolds in the unit sphere

Abstract

An integral inequality for the singular p-laplacian is established for 3/2<p<2. As consequence, lower bounds for the first eigenvalue of the p-laplacian are obtained for minimal submanifolds and prescribed scalar curvature submanifolds in the unit sphere.
Paper Structure (2 sections, 48 equations)

This paper contains 2 sections, 48 equations.

Table of Contents

  1. Introduction
  2. Some preliminaries and key lemmas

Theorems & Definitions (4)

  • proof
  • proof
  • proof
  • proof