PreprintarXiv licencearXiv
A Gage-type estimate for the p-fundamental tone and applications to submanifolds
Abstract
A generalization of the classical Gage's upper bound for the fundamental tone of the Laplacian on complete non-compact Riemannian manifolds to the p-Laplacian context is obtained. As an application, upper estimates for the p-fundamental tone of complete non-compact submanifolds of space forms with constant nonpositive sectional curvature, and for a class of product spaces, are presented.
Related
- An optimal pinching theorem on compact minimal submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices
- Fundamental solutions of the fractional p-Laplacian in cone-like domains, with applications to Liouville-type theorems and global Hölder regularity
- An optimal pinching theorem on compact minimal submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices II
- Type-II Singularities of Immersed Locally Convex Curves Evolving under Generalized Anisotropic Gage Area-Preserving Flows with Slow Curvature Speeds
- Pólya--Szegö Inequality on Submanifolds of Riemannian Manifolds with Nonnegative Curvature and Applications
BibTeX
@misc{soares2026gagetype,
title = {{A Gage-type estimate for the $p$-fundamental tone and applications to submanifolds}},
author = {Matheus Nunes Soares and Fábio reis dos Santos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21877},
eprint = {2609.21877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21877},
}
RIS
TY - UNPB
TI - A Gage-type estimate for the p-fundamental tone and applications to submanifolds
AU - Matheus Nunes Soares
AU - Fábio reis dos Santos
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21877
UR - https://arxiv.org/abs/2609.21877
AB - A generalization of the classical Gage's upper bound for the fundamental tone of the Laplacian on complete non-compact Riemannian manifolds to the p-Laplacian context is obtained. As an application, upper estimates for the p-fundamental tone of complete non-compact submanifolds of space forms with constant nonpositive sectional curvature, and for a class of product spaces, are presented.
ER -