Index and nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces

On embedded minimal surfaces of Costa-Hoffman-Meeks type in hyperbolic space

We present a new construction of embedded minimal surfaces in hyperbolic space with $3$ asymptotically totally geodesic ends and arbitrary finite genus.

一类包含 Costa-Hoffman-Meeks 曲面的高亏格完备极小曲面族

A family of higher genus complete minimal surfaces that includes the Costa-Hoffman-Meeks one

本文构造了一类具有任意高亏格、三个端和有限全曲率的完备浸入极小曲面族，其对称群为二面体群，并在参数满足特定条件时退化为 Costa-Hoffman-Meeks 嵌入极小曲面。

Higher genus Riemann minimal surfaces

We construct higher genus Riemann's minimal surfaces properly embedded in the Euclidean space. To do that we glue end by end a Costa-Hoffman-Meeks examples to two halves genus zero Riemann's minimal surfaces. In first we need to perform a deformation of a Costa-Hoffman-Meeks example to prescribe the flux vector along the catenoidal ends. Then we study the mapping property of the Jacobi operator on the half Riemann example as a perturbation analysis of a CMC-Delaunay half cylinder.

有限亏格的平均曲率流完备嵌入平移孤立子

On complete embedded translating solitons of the mean curvature flow that are of finite genus

本文通过沿 Costa-Hoffman-Meeks 曲面对3个 Grim 抛物面的并集进行去奇化，构造了具有3个端和任意有限亏格的平均曲率流完备嵌入平移孤立子。

Entire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in $\R^3$

We consider minimal surfaces $M$ which are complete, embedded and have finite total curvature in $\R^3$, and bounded, entire solutions with finite Morse index of the Allen-Cahn equation $Δu + f(u) = 0 \hbox{in} \R^3 $. Here $f=-W'$ with $W$ bistable and balanced, for instance $W(u) =\frac 14 (1-u^2)^2$. We assume that $M$ has $m\ge 2$ ends, and additionally that $M$ is non-degenerate, in the sense that its bounded Jacobi fields are all originated from rigid motions (this is known for instance for a Catenoid and for the Costa-Hoffman-Meeks surface of any genus). We prove that for any small $α>0…