一类几何完全非线性抛物型方程的黏性解的唯一性

关于nonlinear elliptic方程奇异解的几点注记III：黏性解，包括抛物算子

Some remarks on singular solutions of nonlinear elliptic equations. III: viscosity solutions, including parabolic operators

本文研究非线性椭圆型方程的奇异解，其中包括黏性解的可去奇点，抛物型方程的Hopf引理的加强，黏性解的强最大值原理和Hopf引理，其中也包括抛物型方程.

关于次极大对称抛物几何的唯一性

On uniqueness of submaximally symmetric parabolic geometries

本文研究抛物几何的对称间隙问题，证明当 $G$ 为秩至少三的复或分裂实单李群以及 $(G,P)=(G_2,P_2)$ 时，次极大对称结构具有局部唯一性。

Modulus of Continuity Estimates for Fully Nonlinear Parabolic Equations

We prove that the moduli of continuity of viscosity solutions to fully nonlinear parabolic partial differential equations are viscosity subsolutions of suitable parabolic equations of one space variable. As applications, we obtain sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations with bounded initial data, via comparison with one-dimensional solutions. This work extends multiple results of Andrews and Clutterbuck for quasilinear equations to fully nonlinear equations.

具有圆填充极限集的Kleinian群的几何有限性和唯一性

Geometric finiteness and uniqueness for Kleinian groups with circle packing limit sets

本文假设$G$是一个无挠生成的非初等Kleinian群，且$Ω(G)$非空.我们证明了$G$的最大可夹元素数恰好是同构于$G$的任何群所包含的最大秩1抛物子群数。一个具有最多秩为1的极大抛物子群的群称为{ \it极大抛物}。我们发现这样的群体存在。我们在这里简明地陈述我们的主要定理。定理I极大抛物群的极限集是一个圆填充，即它的正则集的每个分支都是一个圆盘。定理II.一个极大抛物群是几何有限的。定理III.在$PSL(2,{\bf C})$中，通过其抽象同构类和抛物元确定了一个直至共轭的极大抛物Pinch函数群.

Parabolic frequency for the mean curvature flow

This paper defines a parabolic frequency for solutions of the heat equation along homothetically shrinking mean curvature flows and proves its monotonicity along such flows. As a corollary, frequency monotonicity provides a proof of backwards uniqueness. Additionally, for solutions of more general parabolic equations on mean curvature flow shrinkers, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.

Parabolic frequency on Ricci flows

This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple proof of backwards uniqueness. For solutions of more general parabolic equations on a Ricci flow, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.