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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01334 |
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| _version_ | 1866913083512848384 |
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| author | Bryan, Paul Clutterbuck, Julie Rankin, Cale |
| author_facet | Bryan, Paul Clutterbuck, Julie Rankin, Cale |
| contents | We give simple new proofs of two well-known results for the Schrödinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of the first Dirichlet eigenfunction. Our proof of the first applies to a class of domains including $C^{1,1}$ connected domains and convex potentials. In the special case of convex domains, the second result is a simple corollary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01334 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convexity inequalities for eigenvalues and log-concavity of eigenfunctions Bryan, Paul Clutterbuck, Julie Rankin, Cale Analysis of PDEs 35J20 (Primary) 52A20 (Secondary) We give simple new proofs of two well-known results for the Schrödinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of the first Dirichlet eigenfunction. Our proof of the first applies to a class of domains including $C^{1,1}$ connected domains and convex potentials. In the special case of convex domains, the second result is a simple corollary. |
| title | Convexity inequalities for eigenvalues and log-concavity of eigenfunctions |
| topic | Analysis of PDEs 35J20 (Primary) 52A20 (Secondary) |
| url | https://arxiv.org/abs/2605.01334 |