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Results tagged with geometric-measure-theory
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user 121692
Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
2
votes
Accepted
Does quadratic asymptotic growth imply log-Sobolev inequality?
Suppose that $\lambda > 0$, $f: \mathbb{R}^n \to \mathbb{R}_+$ is $L$-Lipschitz, and define
$$
\mu \left( \mathrm{d} x \right) \propto \exp \left( - \lambda \cdot \| x \|^2 - f\left(x\right) \right).
…
- 801
1
vote
1
answer
88
views
Convergence of probability measures which (asymptotically) concentrate along a submanifold
Let $V : (-1, 1)^d \to \mathbf{R}_+$ be a smooth function, and for $\beta > 0$, define
\begin{align}
P_\beta ( dx ) &= \exp \left( - \beta V ( x ) \right) / z (\beta) \, dx\\
z (\beta) &= \int \exp \ …
- 801
1
vote
0
answers
86
views
Symmetry of the isoperimetric profile
Given a probability measure $\mu$ on a metric space $(X, \mathsf{d})$, the $(\mu-)$Minkowski content of a set $A$ is defined as
$$\mu^+ (A) := {\lim\inf}_{r \to 0^+} \frac{\mu ( A_r \setminus A)}{r},$ …
- 801