Work

p-Eigenvalue pinching sphere theorems

Year: 2026

Type: article

Abstract: In this paper, we establish two p -eigenvalue pinching sphere theorems, for the p -Laplacian, p > 1. The first result states that if the first non-zero p -eigenvalue of a closed Riemannian n -manifold with sectional curvature K M ≥ 1 is sufficiently close to the first non-zero p -eigenvalue of S n then M is homeomorphic to S n . The second states that if the first non-zero p -eigenvalue of a closed Riemannian n -manifold with Ricci curvature R i c M ≥ ( n − 1 ) and injectivity radius inj M ≥ i 0 > 0 is sufficiently close to the first non-zero p -eigenvalue of S n then M is diffeomorphic to S n . Our results extend sphere theorems originally settled for the Laplacian by S. Croke [1] and G.P. Bessa [2] respectively.

Source: Nonlinear Analysis

DOI: 10.1016/j.na.2026.114056

Author: Paulo Henryque C. Silva

Institution: Universidade Federal do Ceará

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,690

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior