First-eigenvalue maximization and inflation of maps
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908395946115072 |
|---|---|
| author | Nayatani, Shin |
| author_facet | Nayatani, Shin |
| contents | Given a compact manifold equipped with a volume element and a Riemannian metric, we formulate and study a dual pair of optimization problems: one concerning smooth maps from the manifold into the Hilbert space $l^2$ and the other concerning the smallest positive eigenvalue of the Bakry-Emery Laplacian. We present examples of manifolds for which these problems can be solved explicitly. We also prove a Nadirashvili-type theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First-eigenvalue maximization and inflation of maps Nayatani, Shin Differential Geometry 58J50, 53C42 Given a compact manifold equipped with a volume element and a Riemannian metric, we formulate and study a dual pair of optimization problems: one concerning smooth maps from the manifold into the Hilbert space $l^2$ and the other concerning the smallest positive eigenvalue of the Bakry-Emery Laplacian. We present examples of manifolds for which these problems can be solved explicitly. We also prove a Nadirashvili-type theorem. |
| title | First-eigenvalue maximization and inflation of maps |
| topic | Differential Geometry 58J50, 53C42 |
| url | https://arxiv.org/abs/2506.05681 |