PreprintarXiv licencearXiv
Spectral properties for critical metrics of the volume functional
Abstract
In this article, we investigate spectral properties of compact V-static manifolds, namely, compact manifolds with boundary whose metrics are critical points of the volume functional under a scalar curvature constraint. We derive sharp estimates for the first Steklov eigenvalue and the entire fourth-order Steklov spectrum. We further obtain a Lichnerowicz-type lower bound for the first eigenvalue of the drifted Laplacian naturally associated with the V-static potential. In the corresponding equality cases, we obtain rigidity results characterizing the Euclidean ball and the hemisphere.
Related
- Non-Kähler Critical Hermitian Metrics of the Dinew--Popovici Functional
- Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian
- Critical metrics for the Dirac-Yamabe eigenvalue ratio and Einstein-Dirac equations
- A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive σk-curvature Metrics
- Limiting properties of Hermitian-Einstein metrics under variation of the Kähler class
BibTeX
@misc{diogenes2026spectral,
title = {{Spectral properties for critical metrics of the volume functional}},
author = {Rafael Diógenes and Jaciane Gonçalves and Ernani Ribeiro Jr},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18717},
eprint = {2609.18717},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18717},
}
RIS
TY - UNPB
TI - Spectral properties for critical metrics of the volume functional
AU - Rafael Diógenes
AU - Jaciane Gonçalves
AU - Ernani Ribeiro Jr
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.18717
UR - https://arxiv.org/abs/2609.18717
AB - In this article, we investigate spectral properties of compact V-static manifolds, namely, compact manifolds with boundary whose metrics are critical points of the volume functional under a scalar curvature constraint. We derive sharp estimates for the first Steklov eigenvalue and the entire fourth-order Steklov spectrum. We further obtain a Lichnerowicz-type lower bound for the first eigenvalue of the drifted Laplacian naturally associated with the V-static potential. In the corresponding equality cases, we obtain rigidity results characterizing the Euclidean ball and the hemisphere.
ER -