We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
L<sup>p</sup>-Minkowski Problem Under Curvature Pinching.
- Authors
Ivaki, Mohammad N; Milman, Emanuel
- Abstract
Let |$K$| be a smooth, origin-symmetric, strictly convex body in |${\mathbb{R}}^{n}$|. If for some |$\ell \in \textrm{GL}(n,{\mathbb{R}})$| , the anisotropic Riemannian metric |$\frac{1}{2}D^{2} \left \Vert \cdot \right \Vert_{\ell K}^{2}$| , encapsulating the curvature of |$\ell K$| , is comparable to the standard Euclidean metric of |${\mathbb{R}}^{n}$| up-to a factor of |$\gamma> 1$| , we show that |$K$| satisfies the even |$L^{p}$| -Minkowski inequality and uniqueness in the even |$L^{p}$| -Minkowski problem for all |$p \geq p_{\gamma }:= 1 - \frac{n+1}{\gamma }$|. This result is sharp as |$\gamma \searrow 1$| (characterizing centered ellipsoids in the limit) and improves upon the classical Minkowski inequality for all |$\gamma < \infty $|. In particular, whenever |$\gamma \leq n+1$| , the even log-Minkowski inequality and uniqueness in the even log-Minkowski problem hold.
- Subjects
EUCLIDEAN metric; CURVATURE; RIEMANNIAN metric; CONVEX bodies; ELLIPSOIDS
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 10, p8638
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad319