Rodrigo Ristow Montes, Jose A. Verderesi
In this paper we introduce the notion of contact angle. We deduce formulas for Laplacian and Gaussian curvature of a minimal surface in $S^{2n+1}$ and give a characterization of the generalized Clifford Torus as the only non-legendrian minimal surface in $S^5$ with constant Contact and Kaehler angles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we discuss the Lagrangian angle and the Kähler angle of immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in $\mathbb C^2$ than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surfaces of constant Kähler angle, together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kähler angle is generally non-vanishing. Secondly, we obtain two pinching results for the Kähler angle which imply rigidity theorems of self-shr…
Parallel mean curvature surfaces with constant contact angle along free boundaries
本文研究了具有常接触角的平行平均曲率曲面，通过分类和构造例子验证了相关定理的准确性。
We show that an immersed minimal annulus, with two planar boundary curves along which the surface meets these planes with constant contact angle, is part of the catenoid.
In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R^3. Also we compute, by using the Taylor expansion, the directions of high contact with hyperspheres of a surface immersed in R^4 and the asymptotic directions of a surface immersed in R^5.
We study properly embedded and immersed p(pseudohermitian)-minimal surfaces in the 3-dimensional Heisenberg group. From the recent work of Cheng, Hwang, Malchiodi, and Yang, we learn that such surfaces must be ruled surfaces. There are two types of such surfaces: band type and annulus type according to their topology. We give an explicit expression for these surfaces. Among band types there is a class of properly embedded p-minimal surfaces of so called helicoid type. We classify all the helicoid type p-minimal surfaces. This class of p-minimal surfaces includes all the entire p-minimal graphs…
We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we will give a characterization of flat minimal surfaces in $S^5$ with constant contact angle.
Assuming that there exists a translating soliton $u_\infty$ with speed $C$ in a domain $Ω$ and with prescribed contact angle on $\partialΩ$, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to $u_\infty +Ct$ as $t\to\infty$. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of $Ω$ and Ricci curvature in $Ω$.
In this paper we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immersed in general 3-manifolds with boundary. We also study noncompact capillary surfaces with finite index and show that, under suitable curvature assumptions, such surface is conformally equivalent to a compact Riemann surface with boundary, punctured at finitely many points. We then prove that a weakly stable capillary surface immersed in a half-space of $\mathbb{R}^3$ which is minimal or has a contact angle less than o…
In this paper we introduce the notion of contact angle for an immersed surface in three dimensional sphere. We deduce formulas for the Laplacian and for the Gaussian curvature, and we classify minimal surfaces in $S^3$ with constant contact angle. Also, we give an example of a minimal surface in $S^3$ with non constant contact angle.
We provide a characterization of the Clifford Torus in S3 via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S3 with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.
We study the prescribed mean curvature equation with a prescribed boundary contact angle condition in $M\times\R$ where $M^n$ is a Riemannian submanifold in $\R^{n+1}$. The main purpose is to establish a priori gradient estimates for solutions, from which the long time existence of the solution are derived.
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
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。
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…
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。
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.
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.
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…
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。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。