User No-one

8 votes

1 answer

479 views

Whitney's approximation theorem for Lipschitz manifolds

asked Feb 9, 2022 at 17:25

8 votes

1 answer

2k views

How badly can the Lebesgue differentiation theorem fail?

asked Sep 5, 2022 at 10:39

8 votes

1 answer

991 views

A seemingly trivial property of differentiable functions

asked Sep 1, 2022 at 19:13

7 votes

0 answers

475 views

A seemingly trivial property of continuous functions differentiable at the origin (PART 2)

asked Sep 1, 2022 at 20:53

6 votes

3 answers

453 views

If the measure theoretic boundary is closed must it coincide with the topological boundary?

asked Sep 16, 2022 at 0:51

5 votes

1 answer

192 views

Is the support of a Sobolev function a varifold?

asked Aug 30, 2022 at 22:45

5 votes

2 answers

526 views

$\frac{\partial f}{\partial \overline{z}}=0$ in distributional sense implies $f$ is holomorphic

asked Feb 1, 2022 at 15:32

5 votes

2 answers

356 views

$C^1$ harmonic functions on a dense open set are globally harmonic

asked Dec 11, 2023 at 6:04

4 votes

1 answer

498 views

$f\in C(B_1)\cap W^{1,2}(B_1\setminus \{f=0\})$ implies $f\in W^{1,2}(B_1)$?

asked Nov 10, 2023 at 20:04

4 votes

1 answer

3k views

An inequality for harmonic functions

asked Dec 2, 2022 at 15:36

3 votes

1 answer

308 views

Each diffusion SDE is associated to a unique family of transition kernels

asked Aug 2, 2023 at 20:15

3 votes

0 answers

411 views

Show that continuous maps between smooth manifolds can be approximated by smooth maps WITHOUT using Whitney's embedding theorem

asked Oct 24, 2022 at 16:00

3 votes

1 answer

502 views

Forgery theorem: the Brownian motion stays close to any curve with positive probability

asked Oct 27, 2022 at 18:51

2 votes

2 answers

198 views

$(1+\epsilon)$-bilipschitz parametrization of Lipschitz manifold

asked Aug 29, 2022 at 12:28

2 votes

0 answers

165 views

A question from Leon Simon's "Lectures on Geometric Measure Theory"

asked Oct 13, 2023 at 6:13

2 votes

1 answer

268 views

If $\mathcal{H}^{n-1}(E)=0$ then $\mathbb{R}^n\setminus E$ is connected

asked Oct 26, 2023 at 0:20

2 votes

2 answers

344 views

Minimal sufficient statistic: a measurability issue in a well-known theorem

asked Jun 7, 2023 at 23:43

2 votes

0 answers

138 views

$\mathscr{H}^{n-2}(\Sigma)< \infty$ implies $\mathscr{H}^{n-1}(\pi(\Sigma))=0$

asked Dec 22, 2023 at 3:25

1 vote

2 answers

203 views

If $\mathcal{H}^{n-1}(K)=0$ then $\mathcal{H}^n(K\times \mathbb{R})=0$

asked Oct 25, 2023 at 23:56

1 vote

1 answer

97 views

$L^p$ function whose graph is not a varifold

asked Sep 1, 2022 at 12:09

0 votes

1 answer

212 views

Does weak convergence in $L^2$ imply convergence a.e. of a subsequence? [closed]

asked Feb 28 at 21:26

Stack Exchange Network

21 Questions

Whitney's approximation theorem for Lipschitz manifolds

How badly can the Lebesgue differentiation theorem fail?

A seemingly trivial property of differentiable functions

A seemingly trivial property of continuous functions differentiable at the origin (PART 2)

If the measure theoretic boundary is closed must it coincide with the topological boundary?

Is the support of a Sobolev function a varifold?

$\frac{\partial f}{\partial \overline{z}}=0$ in distributional sense implies $f$ is holomorphic

$C^1$ harmonic functions on a dense open set are globally harmonic

$f\in C(B_1)\cap W^{1,2}(B_1\setminus \{f=0\})$ implies $f\in W^{1,2}(B_1)$?

An inequality for harmonic functions

Each diffusion SDE is associated to a unique family of transition kernels

Show that continuous maps between smooth manifolds can be approximated by smooth maps WITHOUT using Whitney's embedding theorem

Forgery theorem: the Brownian motion stays close to any curve with positive probability

$(1+\epsilon)$-bilipschitz parametrization of Lipschitz manifold

A question from Leon Simon's "Lectures on Geometric Measure Theory"

If $\mathcal{H}^{n-1}(E)=0$ then $\mathbb{R}^n\setminus E$ is connected

Minimal sufficient statistic: a measurability issue in a well-known theorem

$\mathscr{H}^{n-2}(\Sigma)< \infty$ implies $\mathscr{H}^{n-1}(\pi(\Sigma))=0$

If $\mathcal{H}^{n-1}(K)=0$ then $\mathcal{H}^n(K\times \mathbb{R})=0$

$L^p$ function whose graph is not a varifold

Does weak convergence in $L^2$ imply convergence a.e. of a subsequence? [closed]