On embeddedness of area-minimizing disks, and an application to constructing complete minimal surfaces

Embeddedness of the solutions to the H-Plateau Problem

We generalize Meeks and Yau's embeddedness result on the solutions of the Plateau problem to the constant mean curvature disks. We show that any minimizing H-disk in an H_0-convex domain is embedded for any H in [0,H_0). In particular, for the unit ball B in R^3, this implies that for any H in [0,1], any Jordan curve in the unit sphere bounds an embedded H-disk in B.

Examples of Area Minimizing Surfaces in 3-manifolds

In this paper, we give some examples of area minimizing surfaces to clarify some well-known features of these surfaces in more general settings. The first example is about Meeks-Yau's result on embeddedness of solution to the Plateau problem. We construct an example of a simple closed curve in R^3 which lies in the boundary of a mean convex domain in R^3, but the area minimizing disk in R^3 bounding this curve is not embedded. Our second example shows that Brian White's boundary decomposition theorem does not extend when the ambient space has nontrivial homology. Our last examples show that th…

Area-minimizing cones over minimal embeddings of R-spaces

In this paper, by constructing area-nonincreasing retractions, we prove area-minimizing properties of some cones over minimal embeddings of R-spaces.

关于面积最小锥体的一些配置结果

Some configuration results for area-minimizing cones

本文研究了构造面积最小锥体的配置结果，发现特定条件下的极小子流形和球面的乘积锥体具有面积最小性质，并证明了相关类别的基数相同。

高维螺旋面的稳定性与面积最小化性质

Stability and Area-Minimizing Property of Higher-Dimensional Helicoids

该研究完全确定了高维螺旋面的稳定性与面积最小化性质：当k≥3时稳定，k≤2时不稳定；当k为偶数时面积最小化，k为奇数时非面积最小化，并通过显式校准和竞争者证明。

Laplacian 代数与极小超锥体的子校准

Laplacian Algebras and Subcalibrations for Minimal Hypercones

本文提出基于 Laplacian 代数的代数机制，通过闭包恒等式和代数不等式构造极小超锥体并判定其面积极小性、严格稳定性，应用于等参超锥体及复行列式实部零集，并给出奇次刚性与回拉判据。