2 citations · 2 across the 6 of their papers we have counts for
8 papers
Sheeting property and rigidity for stable solutions to the Allen--Cahn equation
Yong Liu, Tianci Luo, Kelei Wang +3
We prove a sheeting theorem for stable solutions to the Allen--Cahn equation in ambient dimensions through . We show that weak convergence of the measures $\varepsilon|Du_\…
Stable De Giorgi conjecture of the Allen--Cahn equation in
Yong Liu, Tianci Luo, Kelei Wang +3
We prove that every bounded stable entire solution of the Allen--Cahn equation in is one-dimensional. As a consequence, the full De Giorgi conjecture in i…
Alexandrov--Fenchel inequalities for convex domains in the sphere
Tianci Luo, Yong Wei, Rong Zhou
We prove the Alexandrov--Fenchel inequalities between any two spherical quermassintegrals for smooth weakly convex domains contained in an open hemisphere, with equality if and onl…
Positive -bi-Ricci curvature and Mean curvature flow with surgery in hyperbolic space
Tianci Luo, Yong Wei, Rong Zhou
Let and . We prove that every smooth closed connected immersed hypersurface in hyperbolic space whose induced metric has positive -bi-Ricci curvature admit…
Free boundary flows by powers of the Gauss curvature in the unit ball
Tianci Luo, Yong Wei, Rong Zhou
We study smooth compact strictly convex hypersurfaces in the unit ball that meet the support sphere orthogonally and evolve by the -Gauss curvature flow , $α>…
Contraction of hypersurfaces with positive sectional curvature in hyperbolic space
Tianci Luo, Yong Wei, Rong Zhou
We study contracting curvature flows of compact hypersurfaces with positive sectional curvature in hyperbolic space . The speed is assumed to be homogeneous of de…
The horospherical -Christoffel-Minkowski problem in hyperbolic space
Tianci Luo, Yong Wei
The horospherical -Christoffel-Minkowski problem was posed by Li and Xu (2022) as a problem prescribing the -th horospherical -surface area measure of -convex domains i…
Gauss curvature type flow and Alexandrov-Fenchel inequalities in the hyperbolic space
Tianci Luo, Rong Zhou
We consider the Gauss curvature type flow for uniformly convex hypersurfaces in the hyperbolic space . We prove that if the initial closed hypersu…