Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.14735 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912455608762368 |
|---|---|
| author | Li, Xiao Nguyen, Nguyen Dac Khoi Ye, Deping |
| author_facet | Li, Xiao Nguyen, Nguyen Dac Khoi Ye, Deping |
| contents | The notions of the Euclidean surface area measure and the spherical surface area measure of $α$-concave functions in $\mathbb{R}^n$, with $-\frac{1}{n}<α<0$, are introduced via a first variation of the total mass functional with respect to the $α$-sum operation. Subsequently, these notions are extended to those for $α$-concave measures. We then study the Minkowski problem associated with the Euclidean surface area measures of $α$-concave measures via optimal transport. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Minkowski problem for $α$-concave functions via optimal transport Li, Xiao Nguyen, Nguyen Dac Khoi Ye, Deping Functional Analysis Analysis of PDEs Metric Geometry 26B25, 52A40, 52A41, 35G20, 31B99 The notions of the Euclidean surface area measure and the spherical surface area measure of $α$-concave functions in $\mathbb{R}^n$, with $-\frac{1}{n}<α<0$, are introduced via a first variation of the total mass functional with respect to the $α$-sum operation. Subsequently, these notions are extended to those for $α$-concave measures. We then study the Minkowski problem associated with the Euclidean surface area measures of $α$-concave measures via optimal transport. |
| title | A Minkowski problem for $α$-concave functions via optimal transport |
| topic | Functional Analysis Analysis of PDEs Metric Geometry 26B25, 52A40, 52A41, 35G20, 31B99 |
| url | https://arxiv.org/abs/2506.14735 |