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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...
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...
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...