English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we study the locally constrained inverse curvature flow forhypersurfaces in the half-space with $\theta$-capillary boundary, which wasrecently introduced by Wang-Weng-Xia. Assume that the initial hypersurface isstrictly convex with the contact angle $\theta\in (0,\pi/2]$. We prove that thesolution of the flow remains to be strictly convex for $t>0$, exists for allpositive time and converges smoothly to a spherical cap. As an application, weprove a complete family of Alexandrov-Fenchel inequalities for convex capillaryhypersurfaces in the half-space with the contact angle $\theta\in(0,\pi/2]$.Along the proof, we develop a new tensor maximum principle for parabolicequations on compact manifold with proper Neumann boundary condition.

A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space