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Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements
Matrix completion The Dantzig selector oracle inequalities norm of random matrices convex optimization and semidefinite programming
2015/6/17
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
Minimal surface systems, maximal surface systems, and special Lagrangian equations
minimal submanifold special Lagrangian equation entire solution
2012/4/17
We extend Osserman's lemma on the generalized Gauss map of two-dimensional minimal graphs of higher codimension, construct a Jenkins-Serrin type special Lagrangian Scherk graph explicitly, and general...
Interior partial regularity for minimal Lp-vectorfields with integer fluxes
Interior partial regularity minimal Lp-vectorfields integer fluxes
2012/4/17
We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-energy. More precisely, we prove that the minimal...
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...
Some Singular Limit Laminations of Embedded Minimal Planar Domains
Singular Limit Laminations Embedded Minimal Planar Domains Differential Geometry
2011/9/15
Abstract: In this paper we give two examples of sequences of embedded minimal planar domains in $\mathbb{R}^3$ which converge to singular laminations of $\mathbb{R}^3$. In contrast with the situation ...
Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
Quantitative Stratification the Regularity of Harmonic Maps Minimal Currents
2011/9/9
Abstract: We introduce techniques for turning estimates on the infinitesimal behavior of solutions to nonlinear equations (statements concerning tangent cones and blow ups) into more effective control...
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...
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
Duffin-Kemmer-Petiau theory nonminimal coupling Klein’s paradox
2010/12/1
The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and
nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Ke...
We prove that the specialization to q = 1 of a Kirillov-Reshetikhin module for an untwisted
quantum affine algebra of classical type is projective in a suitable category. This
yields a uniform chara...
We establish a classification of cubic minimal cones in case of the so-called radial
eigencubics. Our principal result states that any radial eigencubic is either a member of the
infinite family of ...
EQUIVARIANT LAGRANGIAN MINIMAL S^3 IN CP^3
complex projective space equivariant lagrangian minimal submanifold
2007/12/12
Equivariant Lagrangian minimal immersion of $S^3$ into $\bbc P^3$ is studied. The complete classification and analytic expression for such kind of immersions are given.
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...
Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to...