PreprintarXiv licencearXiv
A sharp curvature lower bound for the first exterior p-harmonic Steklov eigenvalue
Abstract
In this paper, we study the first variational Steklov eigenvalue of the $ p$-Laplace equation on exterior domain $ Ω^{\text{ext}}$ for $ 1< p <n$. If $ Ω$ is convex and $ \partial Ω\in C^{1,1}$, we prove a sharp lower bound in terms of p-logarithmic mean of the principal curvatures of $ \partial Ω$. For the linear case $ p=2$, our estimate reduces to the logarithmic mean bound of Bundrock et al. (arXiv:2511.09490). We also derive an upper bound in terms of a boundary isocapacitary constant. The analysis relies on the established finite energy theory on exterior domains, together with a decay estimate for p-harmonic extensions.
Related
- Discreteness of the Steklov Spectrum for Exterior Non-Compact Free-Boundary Minimal Surfaces with Regular Ends of Finite Total Curvature
- Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface
- Sharp lower bound of the first eigenvalue of the p-Laplacian under integral Ricci curvature
- A sharp two-disk bound for the second positive Neumann eigenvalue under a curvature upper bound
- The exterior Steklov problem for Euclidean domains
BibTeX
@misc{niu2026sharp,
title = {{A sharp curvature lower bound for the first exterior p-harmonic Steklov eigenvalue}},
author = {Yating Niu and Tao Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11517},
eprint = {2609.11517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11517},
}
RIS
TY - UNPB
TI - A sharp curvature lower bound for the first exterior p-harmonic Steklov eigenvalue
AU - Yating Niu
AU - Tao Wang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11517
UR - https://arxiv.org/abs/2609.11517
AB - In this paper, we study the first variational Steklov eigenvalue of the $ p$-Laplace equation on exterior domain $ Ω^{\text{ext}}$ for $ 1< p <n$. If $ Ω$ is convex and $ \partial Ω\in C^{1,1}$, we prove a sharp lower bound in terms of p-logarithmic mean of the principal curvatures of $ \partial Ω$. For the linear case $ p=2$, our estimate reduces to the logarithmic mean bound of Bundrock et al. (arXiv:2511.09490). We also derive an upper bound in terms of a boundary isocapacitary constant. The analysis relies on the established finite energy theory on exterior domains, together with a decay estimate for p-harmonic extensions.
ER -