# Lectures on Minimal Surface Theory

@article{White2013LecturesOM, title={Lectures on Minimal Surface Theory}, author={Brian White}, journal={arXiv: Differential Geometry}, year={2013} }

An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.

## 12 Citations

### Non existence of Type II singularities for embedded and unknotted space curves

- Mathematics
- 2016

In this paper we prove that a certain class of embedded unknotted curves in $\mathbb{R}^3$ evolving under curve shortening flow do not form singularities Type II before collapsing to a point. Our…

### The extension problem of the mean curvature flow (I)

- MathematicsInventiones mathematicae
- 2019

AbstractWe show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in $${{\mathbb {R}}}^3$$R3.

### Contractible $3$-manifold and Positive scalar curvature (I)

- Mathematics
- 2019

In this work we prove that the Whitehead manifold has no complete metric of positive scalar curvature. This result can be generalized to the genus one case. Precisely, we show that no contractible…

### Minimal 2-Spheres in 3-Spheres with Arbitrary Metric

- Mathematics
- 2020

In this paper, we prove that the $3$-sphere endowed with an arbitrary Riemannian metric contains at least two embedded minimal $2$-spheres. This improves results of White (Indiana Univ. Math. J.…

### Gaussian curvature, elasticity of string and geodesic incompleteness in string theory

- Mathematics
- 2015

In classical general relativity, singularity theorems are concerned with the existence of an incomplete inextendible nonspacelike geodesic. We prove the incompleteness of a geodesic surface under…

### On the distance from the origin to an entire graphic m-shrinker

- Mathematics
- 2021

Let Σ be an entire graphic m-shrinker in R and X be the position vector field of Σ. By using the generalized divergence theorem, we obtain a formula for the weighted volume of Σ that is related to X,…

### Necessary conditions and nonexistence results for connected submanifolds in a Riemannian manifold

- Mathematics
- 2017

### Six proofs of the F\'ary--Milnor theorem

- Mathematics
- 2022

It is known for many proofs based on different ideas. We sketch several solutions, one solution per section; each can be read independently. This problem also has a number of refinements and…

### Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds

- Mathematics
- 2016

We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquely…

### Quantitative flatness results and $BV$-estimates for stable nonlocal minimal surfaces

- MathematicsJournal of Differential Geometry
- 2019

We establish quantitative properties of minimizers and stable sets for nonlocal interaction functionals, including the $s$-fractional perimeter as a particular case.
On the one hand, we establish…

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