https://neckpinch.com/authors/rongli-huang/New arXiv papers by Rongli Huang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2505.23067arxiv:2505.23067Thu, 29 May 2025 00:00:00 GMTRongli Huang, Changzheng Qu, Zhizhang Wang, Weifeng Wo — We investigate the evolution of strictly convex hypersurfaces driven by the k-Hessian curvature flow, subject to the second boundary condition. We first explore the translating solutions corresponding to this boundary value problem. Next, we establish the long-time existence of the flow and prove that it converges to a translating solution. To overcome the difficulty of driving boundary C² estimates, we employ an orthogonal invariance technique. Using this method, we extend the results of Schnürer-Smoczyk and Schnürer from the second boundary value problem of Gauss curvature flow to k-Hessian curvature flow.Other curvature flowsGauss curvature flowSelf-shrinkers & translatorsBoundaries & non-compactLong-time existence & convergence https://arxiv.org/abs/2410.17794arxiv:2410.17794Wed, 23 Oct 2024 00:00:00 GMTShanshan Li, Jiaru Lv, Rongli Huang — In this paper, we consider the mean curvature flow of entire Lagrangian graphs with initial data in the pseudo-Euclidean space, which is related to the special Lagrangian parabolic equation. We show that the parabolic equation has a smooth solution u(x,t) for three corresponding nonlinear equations between the Monge-Ampgraveere type equation(τ=0) and the special Lagrangian parabolic equation(τ=fracπ2). Furthermore, we get the bound of D^lu, l=\3,4,5,⋯\ for τ=fracπ4 and the decay estimates of the higher order derivatives when 0<τ<fracπ4 and fracπ4<τ<fracπ2. We also prove that u(x,t) converges to smooth self-expanding solutions of.Mean curvature flowLagrangian mean curvature flowSelf-shrinkers & translators https://arxiv.org/abs/2404.05972arxiv:2404.05972Tue, 09 Apr 2024 00:00:00 GMTRongli Huang — This is a sequel to [2] and [3], which study the second boundary value problems for mean curvature flow. Consequently, we construct the translating solitons with prescribed Gauss image in Minkowski space.Mean curvature flowSelf-shrinkers & translators