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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Gauss maps of complete minimal surfaces in Rm
Rm 完全极小曲面 高斯映射
2023/12/11
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3
Allen-Cahn Equation Embedded Minimal Surfaces Finite Total Curvature in R3
2015/4/3
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3.
Isometric deformations of minimal surfaces in $S^{4}$
Minimal surfaces in S4 isometric deformation normal curvature function
2012/3/1
We consider the isometric deformation problem for oriented non simply connected immersed minimal surfaces $f:M \to S^{4}$. We prove that the space of all isometric minimal immersions of $M$ into $S^{4...
Construction of minimal surfaces with special type ends
minimal surface total curvature end winding order
2011/9/28
We proved that there exists a family of complete oriented minimal surfaces in $R^3$ with finite total curvature $-4n\\pi$, each of which has 0 genus and two ends, and both of the ends have winding ord...
Doubling and Desingularization Constructions for Minimal Surfaces
Differential geometry minimal surfaces partial differential equations
2011/2/28
In the first part of the paper we discuss the current status of the application of the gluing methodology to doubling and desingularization constructions for minimal surfaces in Riemannian three-manif...
Bumpy Riemannian metrics and closed parametrized minimal surfaces in Riemannian manifolds
Bumpy Riemannian metrics closed parametrized minimal surfaces Riemannian manifolds
2011/2/22
This article is concerned with conformal harmonic maps f : ! M,where is a closed Riemann surface and M is a compact Riemannian manifold of dimension at least four. We show that when the ambient ma...
A Laguerre minimal surface is an immersed surface in the Euclidean space being an extremal of the functional \int (H^2/K - 1) dA. In the present paper, we prove that the only ruled Laguerre minimal s...
On complete stable minimal surfaces in 4-manifolds with positive isotropic curvature
minimal surfaces 4-manifolds positive isotropic curvature
2010/11/12
We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly posi...
We consider immersions of a Riemann surface into a manifold with $G_2$-holonomy and give criteria for them to be conformal and harmonic, in terms of an associated Gauss map
For any m > 1, we construct properly embedded minimal surfaces in H2 R with genus zero,
infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable nu...
On minimal surfaces of axially symmetric planal Riemannian metrics in 3-space
Riemannian metrics Minimal surfaces
2010/9/17
In last, we characterise that, the only riemannian metrics which have a constant determinant on Bμ,ξ and which admit all the planes as minimal surfaces are Heisenberg’s metrics.
Weierstrass representation formulae of minimal surfaces in $H_3$ and $H^2\times R$
Minimal immersions Weierstrass representation Heisenberg group Hyperbolic space
2007/12/11
We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the t...