A fully nonlinear locally constrained anisotropic curvature flow

A Fully Nonlinear Conformal Flow on Locally Conformally Flat Manifolds

We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we solve the σk-Yamabe problem for locally conformal flat manifolds when k 6= n/2.

On Anisotropic Curvature Flow Equations

We study the anisotropic flow V = bk where b > 0. We prove that if 13 < σ ≤ 1, only type I blow up occurs and if 0 < σ < 13 Type II blow up occurs. We also establish a prior estimates and existence of stationary solutions of self-similar curves and the existence of “ Abresch-Langer” type curves.

Non-collapsing in fully nonlinear curvature flows

We consider embedded hypersurfaces evolving by fully nonlinear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a noncollapsing estimate: Precisely, the function which gives the curvature of the largest interior sphere touching the hypersurface at each point is a subsolution of the linearized flow equation i...

Discrete anisotropic curvature flow of graphs

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Anisotropic and Crystalline Mean Curvature Flow