Alexandrov–Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-
space. Then we solve the related isoperimetric type problems for the convex capillary …
space. Then we solve the related isoperimetric type problems for the convex capillary …
Locally constrained inverse curvature flows
J Scheuer, C Xia - Transactions of the American Mathematical Society, 2019 - ams.org
We consider inverse curvature flows in warped product manifolds, which are constrained
subject to local terms of lower order—namely, the radial coordinate and the generalized …
subject to local terms of lower order—namely, the radial coordinate and the generalized …
Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere
M Makowski, J Scheuer - arXiv preprint arXiv:1307.5764, 2013 - arxiv.org
We prove a rigidity result in the sphere which allows us to generalize a result about smooth
convex hypersurfaces in the sphere by Do Carmo-Warner to convex $ C^ 2$-hypersurfaces …
convex hypersurfaces in the sphere by Do Carmo-Warner to convex $ C^ 2$-hypersurfaces …
Hyperbolic -sum and Horospherical -Brunn-Minkowski theory in hyperbolic space
H Li, B Xu - arXiv preprint arXiv:2211.06875, 2022 - arxiv.org
The classical Brunn-Minkowski theory studies the geometry of convex bodies in Euclidean
space by use of the Minkowski sum. It originated from H. Brunn's thesis in 1887 and H …
space by use of the Minkowski sum. It originated from H. Brunn's thesis in 1887 and H …
Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the
$(n+ 1) $-dimensional Euclidean unit ball. Then we solve some related isoperimetric type …
$(n+ 1) $-dimensional Euclidean unit ball. Then we solve some related isoperimetric type …
Alexandrov-Fenchel type inequalities in the sphere
M Chen, J Sun - Advances in Mathematics, 2022 - Elsevier
In this paper, we proved the Alexandrov-Fenchel inequalities for embedded, closed,
connected and convex C 2-hypersurfaces in S n+ 1: A k≥ ξ k, k− 2 (A k− 2) for any 1≤ k≤ …
connected and convex C 2-hypersurfaces in S n+ 1: A k≥ ξ k, k− 2 (A k− 2) for any 1≤ k≤ …
A complete family of Alexandrov–Fenchel inequalities for convex capillary hypersurfaces in the half-space
In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the
half-space with θ-capillary boundary, which was recently introduced by Wang et al.(Math …
half-space with θ-capillary boundary, which was recently introduced by Wang et al.(Math …
[HTML][HTML] Harmonic mean curvature flow and geometric inequalities
We employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in
hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals …
hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals …
Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
Y Hu, H Li - Advances in Mathematics, 2023 - Elsevier
In this paper, we prove a family of identities for smooth closed and strictly convex
hypersurfaces in the sphere and hyperbolic/de Sitter space. As applications, we prove …
hypersurfaces in the sphere and hyperbolic/de Sitter space. As applications, we prove …
On an inverse curvature flow in two-dimensional space forms
We study the evolution of compact convex curves in two-dimensional space forms. The
normal speed is given by the difference of the weighted inverse curvature with the support …
normal speed is given by the difference of the weighted inverse curvature with the support …