# Questions tagged [minimal-surfaces]

For questions about minimal surfaces in the sense of Riemannian geometry (as opposed to complex geometry).

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### Asymptotic of positive solution to elliptic equation

I am reading the paper "Area minimizing hypersurfaces with isolated singularities" by Hardt and Simon (https://eudml.org/doc/152770) and I get stuck on equation 1.9 on page 106. The ...
1 vote
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### Minimal surface enclosing balls

(This question is tangentially related to an earlier question I posed: Minimal surface enclosing two congruent balls.) Let $B_1,\ldots,B_k$ be unit-radius balls in $\mathbb{R}^3$, with pairwise ...
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### Minimal surface enclosing two congruent balls

Let $B_1$ and $B_2$ be two unit-radius balls in $\mathbb{R}^3$ whose centers are separated by a distance $d \ge 2$. Q. For sufficiently small $d$, is the minimal area surface enclosing $B_1$ and $B_2$...
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### How to interpret this quote of Lin?

I recently stumbled across a quote of Fang-Hua Lin that I have trouble understanding [1, page 42]. It is a well-known fact that a weakly converging sequence of stationary integral currents may have a ...
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### Is every minimal graph smooth?

The following result was taken from the book of Gilbarg-Trudinger: In particular, if the graph is minimal, then $u$ is smooth. Now comes my question: does the same conclusion hold for graphs over ...
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### Finding metric to make a submanifold minimal

I would like to ask a question, which I am not sure if there exist some known results (that I could not locate). Given a smooth embedded submanifold $M$ in $\mathbb R^n,$ is it always possible to find ...
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### Minimizing area in relative homology class

A well known result in geometric measure theory asserts that if $(M^{n+1}, g)$ is a closed Riemannian manifold and $\alpha \in H_n(M)$ is a nonzero homology class, then there exists a closed embedded ...
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### Minimal graph over convex domain is area-minimizing

I am looking for a reference stating that If a graph $z=f(x,y)$ over a convex domain $D$ is minimal, then it is area-minimizing. 5.4.18 in Federer's "Geometric measure theory" and Lemma 1.1. in ...