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Asymptotics for the k-Hessian Eigenvalue on the Unit Ball
Abstract
We compute the limit of the eigenvalue of the k-Hessian operator on the unit ball in ℝn when k→ ∞, assuming that the ratio n/k remains fixed. When n< 2ke, we moreover identify the limit of the corresponding eigenfunctions. We also derive monotonicity results and consider when the ratio varies in n.
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BibTeX
@misc{mccleerey2026asymptotics,
title = {{Asymptotics for the $k$-Hessian Eigenvalue on the Unit Ball}},
author = {Nicholas McCleerey and Abhinav Pande and Thidas Wanasinghe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05277},
eprint = {2609.05277},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05277},
}
RIS
TY - UNPB
TI - Asymptotics for the k-Hessian Eigenvalue on the Unit Ball
AU - Nicholas McCleerey
AU - Abhinav Pande
AU - Thidas Wanasinghe
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05277
UR - https://arxiv.org/abs/2609.05277
AB - We compute the limit of the eigenvalue of the k-Hessian operator on the unit ball in ℝ^n when k→ ∞, assuming that the ratio n/k remains fixed. When n< 2ke, we moreover identify the limit of the corresponding eigenfunctions. We also derive monotonicity results and consider when the ratio varies in n.
ER -