4 papers
Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditions
Linlin Fan, Peibiao Zhao
Wang, Weng and Xia[Math. Ann. 388 (2024), no. 2] studied a mean curvature type flow for the smooth, embedded capillary hypersurfaces with a constant contact angle and c…
Legendrian curve flow in Sasakian sub-Riemannian 3-manifolds
Jingshi Cui, Peibiao Zhao
In this paper, we introduce a kind of inverse mean curvature flow (1.2) in a Sasakian sub-Riemannian 3-manifold for Legendrian curves, which slightly differs from the classical…
Hopf's lemma for parabolic equations involving a generalized tempered fractional -Laplacian
Linlin Fan, Linfen Cao, Peibiao Zhao
In this paper, we study a nonlinear system involving a generalized tempered fractional -Laplacian in : \begin{equation*} \left\{ \begin{array}{ll} \partial_tu(x,t)+(-Δ…
Michael-Simon type inequalities in hyperbolic space via Brendle-Guan-Li's flows
Jingshi Cui, Peibiao Zhao
In the present paper, we first establish and verify a new sharp hyperbolic version of the Michael-Simon inequality for mean curvatures in hyperbolic space based…