The $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918115926867968 |
|---|---|
| author | Cabezas-Moreno, Carlos Hu, Jinrong |
| author_facet | Cabezas-Moreno, Carlos Hu, Jinrong |
| contents | In this paper, we investigate an $L_{p}$ Christoffel-Minkowski-type problem that prescribes a class of $L_p$ geometric measures, which are mixtures of the $k$-th area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for $1 < p < q \leq k + 1$, where $1 \leq k \leq n$ and $n \geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$ Cabezas-Moreno, Carlos Hu, Jinrong Analysis of PDEs Differential Geometry In this paper, we investigate an $L_{p}$ Christoffel-Minkowski-type problem that prescribes a class of $L_p$ geometric measures, which are mixtures of the $k$-th area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for $1 < p < q \leq k + 1$, where $1 \leq k \leq n$ and $n \geq 1$. |
| title | The $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$ |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2504.04931 |