Questions tagged [geometric-measure-theory]

It's well known that $C^1$ minimal surfaces (surfaces that are locally area minimzing) in $\mathbb{R}^n$ are automatically smooth, and one can prove this result by solving the Dirichlet problem of the ...

It is a well-known results by Federer and Fleming that there exists at least one mass-minimizing normal current in every real homology class of a closed $n$-dimensional Riemannian manifold $M$. Their ...

I want to know if it is possible to have a general rule for approximating the perimeter of a set $E\subset \mathbb{R}^n$ with finite perimeter in terms of the volume (Lebesgue measure) of a sequence ...

A function $f: \mathbb R^n \to \mathbb R$ is said to be a strict contraction if $$|f(x) - f(y)| < |x - y|$$ for all $x \neq y$. A function $f$ is said to be eikonal if it is differentiable ...

By Rademacher’s theorem, Lipschitz functions are differentiable almost everywhere. I am wondering how badly this pointwise differentiability fails for functions that “just barely” fail to be Lipschitz....