相关论文: The Cauchy problem for Lie-minimal surfaces

We study nonlocal minimal surfaces as a new approximation theory for the area functional, and more specifically in the context of Yau's conjecture on the existence of minimal surfaces in closed three-dimensional manifolds. This programme…

In this paper, we study existence and uniqueness of solutions to Jenkins-Serrin type problems on domains in a Riemannian surface. In the case of unbounded domains, the study is focused on the hyperbolic plane.

Consider the surface quasi-geostrophic equation with random diffusion, white in time. We show global existence and uniqueness in high probability for the associated Cauchy problem satisfying a Gevrey type bound. This article is inspired by…

Stochastic parabolic integro-differential problem is considered in the whole space. By verifying H\"ormander condition, the existence and uniqueness is proved in Lp-spaces of functions whose regularity is defined by a scalable Levy measure.…

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

In this paper, we shall study the Dirichlet problem for the minimal surfaces equation. We prove some results about the boundary behaviour of a solution of this problem. We describe the behaviour of a non-converging sequence of solutions in…

A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…

In this paper, we consider Legendre trajectories of trans-$S$-manifolds. We obtain curvature characterizations of these curves and give a classification theorem. We also investigate Legendre curves whose Frenet frame fields are linearly…

This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a…

This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric functions on Riemannian manifolds, including exotic spheres. The existences and…

In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The…

We study the problem of finding a minimal graph with prescribed boundary data in arbitrary dimension and codimension. Existence, uniqueness, stability and regularity are treated. We first present the well-known results for codimension one:…

In this paper, we investigate a Kazdan-Warner problem on compact K\"ahler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact K\"ahler surfaces when the…

We study surfaces of constant positive Gauss curvature in Euclidean 3-space via the harmonicity of the Gauss map. Using the loop group representation, we solve the regular and the singular geometric Cauchy problems for these surfaces, and…

We prove a theorem concerning the Noether symmetries for the area minimizing Lagrangian under the constraint of a constant volume in an n-dimensional Riemannian space. We illustrate the application of the theorem by a number of examples.

Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we…

Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. The…

In this paper, we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by the period. These surfaces are constructed by adding a handle to the toroidal half-plane layers defined by H.…

There seems to be quite a bit of room for interesting things related to surfaces M in C^m with real dimension m which are totally real and aspects of several complex variables on C^m around M. A basic case occurs when m = 1, with Cauchy…

In this paper we consider the entire weak solutions of the equations for stationary flows of shear thickening fluids in the plane and prove Liouville theorem under the global boundedness condition of velocity fields.