相关论文: Minimal Surfaces from Monopoles

We construct embedded closed minimal surfaces in the round three-sphere, resembling two parallel copies of the Clifford torus, joined by m^2 small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.

We classify all surfaces with constant Gaussian curvature $K$ in Euclidean $3$-space that can be expressed as an implicit equation of type $f(x)+g(y)+h(z)=0$, where $f$, $g$ and $h$ are real functions of one variable. If $K=0$, we prove…

We prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed Riemannian manifolds in terms of their index and area, restricting to the case where the hypersurface has dimension less than seven. In…

The normal map given by Birkhoff orthogonality yields extensions of principal, Gaussian and mean curvatures to surfaces immersed in three-dimensional spaces whose geometry is given by an arbitrary norm and which are also called Minkowski…

Let $\mathbb{M}^{2}$ be a complete non compact orientable surface of non negative curvature. We prove in this paper some theorems involving parabolicity of minimal surfaces in $\mathbb{M}^{2}\times\mathbb{R}$. First, using a…

In 2004, Taubes introduced the space of minimal hyperbolic germs with elements consisting of the first and second fundamental form of an equivariant immersed minimal disk in hyperbolic 3-space. Herein, we initiate a further study of this…

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…

In this paper we present the novel method for the generation of periodic embedded surfaces of nonpositive Gaussian curvature. The structures are related to the local minima of the scalar order parameter Landau-Ginzburg hamiltonan for…

We study global aspects of the mean curvature flow of non-separating hypersurfaces $S$ in closed manifolds. For instance, if $S$ has non-vanishing mean curvature, we show its level set flow converges smoothly towards an embedded minimal…

In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal…

We consider harmonic immersions in $\R^{\N}$ of compact Riemann surfaces with finitely many punctures where the harmonic coordinate functions are given as real parts of meromorphic functions. We prove that such surfaces have finite total…

We study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in close planes of Euclidean 3-space. Our main result is a classification of these minimal surfaces, under certain…

The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the…

Given $I,B\in\mathbb{N}\cup \{0\}$, we investigate the existence and geometry of complete finitely branched minimal surfaces $M$ in $\mathbb{R}^3$ with Morse index at most $I$ and total branching order at most $B$. Previous works of…

In this paper we investigate free boundary minimal surfaces in the unit ball in Euclidean 3-space, and by using holomorphic techniques we prove that intersection curves of free boundary minimal surfaces with the unit sphere are all circles.

The Riemannian product of two hyperbolic planes of constant Gaussian curvature -1 has a natural K\"ahler structure. In fact, it can be identified with the complex hyperbolic quadric of complex dimension two. In this paper we study…

In this paper we characterize logarithmic surfaces which admit K\"ahler-Einstein metrics with negative scalar curvature and small edge singularities along a normal crossing divisor.

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural…

We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius. We illustrate it by obtaining some…

In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat torus must be…