# Questions tagged [minimal-surfaces]

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

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### Convergence of free boundary minimal surfaces

I suspect the following statement is true: Let $(M^3,g)$ be a compact and orientable Riemannian $3$-manifold with nonempty boundary. Let $\{\Sigma_n\}_{n \geq 1}$ be a sequence of compact and ...
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### Is every minimal hypersurface in $S^n$ algebraic?

Let $S^n$ be the round n-sphere. Wu-yi Hsiang asked in his paper “Remarks on closed minimal submanifolds in the standard riemannian m-sphere” (1967) the follow question Is every minimal ...
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### Special Riemannian metric on the product

Let $M^2$ be an orientable surface with boundary endowed with a Riemannian metric $g$. We know that if we put in the manifold $M \times \mathbb{R}$ the product metric $\overline{g} = g + dt^2$, then ...
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### maximal surface, parametric approach

I am interesting in maximal surfaces: space-like surface in Minkowsky $\mathbb{R}^{2,1}$ (or De Sitter $dS^3$). Of course space-like implies locally graph and almost all the literature is interested ...
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### Compactness theorem for minimal surfaces

I am a bit confused about the statement of Theorem 1.1 in this paper by Brian White. For convenience, I will restate it here. Theorem: Let $\Omega$ be an open subset of a Riemannian $3$-manifold. ...
In this Inventiones Mathematicae paper, Fischer-Colbrie proved the following result (Proposition 1): Proposition: Let $M$ be a complete two-sided minimal surface in a three manifold $N$. Then if $M$...