A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant Contact Angle

Noncommutative integrability and action-angle variables in contact geometry

We introduce a notion of the noncommutative integrability within a framework of contact geometry.

$\mathbb R^3$ 中具有预定接触角的液滴的最小化运动与光滑平均曲率流的一致性

Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact-angle in $\mathbb R^3$

该研究证明了三维空间中带预定接触角液滴的最小化运动解与光滑平均曲率流等价，为两类平均曲率运动描述建立了一致性。

Nonparametric mean curvature type flows of graphs with contact angle conditions

In this paper we study nonparametric mean curvature type flows in $M\times\mathbb{R}$ which are represented as graphs $(x,u(x,t))$ over a domain in a Riemannian manifold $M$ with prescribed contact angle. The speed of $u$ is the mean curvature speed minus an admissible function $ψ(x,u,Du)$. Long time existence and uniformly convergence are established if $ψ(x,u, Du)\equiv 0$ with vertical contact angle and $ψ(x,u,Du)=h(x,u)ω$ with $h_u(x,u)\geq h_0>0$ and $ω=\sqrt{1+|Du|^2}$. Their applications include mean curvature type equations with prescribed contact angle boundary condition and the asymp…

固定接触角的平稳 varifold 对的边界极大值原理

A boundary maximum principle for stationary pairs of varifolds with fixed contact angle

本文研究带光滑边界的紧 Riemannian 流形中满足固定接触角条件的平稳 varifold 对，并为其建立边界极大值原理。

Global stability of traveling waves for an area preserving curvature flow with contact angle condition

We consider an evolving plane curve with two endpoints that can move freely on the $x$-axis with generating constant contact angles. We discuss the asymptotic behavior of global-in-time solutions when the evolution of this plane curve is governed by area-preserving curvature flow equation. The main result shows that any moving curve converges to a traveling wave if the moving curve starts from an embedded convex curve and remains bounded in global time.

A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle

We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolving family of curves driven by curve diffusion flow, which has free boundary points supported on a line. The evolving curve has fixed contact angle $α\in (0, π)$ with that line and satisfies a no-flux condition. The proof is led by contradiction: A compactness argument combined with the short time existence result enables us to extend the flow, which contradicts the maximality of the solution.

Mean Curvature Motion of Graphs with Constant Contact Angle and Moving Boundaries

We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic equation with a free boundary, and derive a continuation criterion based on the second fundamental form. If the initial graph is concave, we show this is preserved, and that the solution exists only for finite time. This corresponds to a symmetric version of triple junction motion of hypersurfaces by mean curvature, with constant angles at th…

具有固定接触角的相变梯度流

Gradient flow of phase transitions with fixed contact angle

该研究针对能量有界初始数据，分析固定边界接触角下Allen-Cahn方程的相变梯度流，建立解与能量测度的收敛性质，推导Ilmanen型单调性公式，完善了边界接触角相关的梯度流理论。

通过椭圆正则化求解具指定接触角的弱平均曲率流的存在性

Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization

本文通过Ilmanen正则化，将其扩展到毛细现象领域并推导对应一阶变分估计，证明了满足θ∈(0,π)指定接触角的Brakke型弱平均曲率流的存在性。

任意余维数中具有给定平均曲率和接触角的圆盘的存在性

Existence of disks with prescribed mean curvature and contact angle in arbitrary codimension

本文在任意余维数下建立极小极大理论，证明在适当假设下存在具有给定平均曲率和接触角的非恒定分支浸入圆盘或球面，并在欧氏空间中给出自由边界圆盘及维数相关的莫尔斯指标界。