User Anton Petrunin

4 votes

Is there a coordinate-free proof of the hamiltonian character of the geodesic flow?

answered Oct 24, 2020 at 1:46

4 votes

Accepted

Is the barycenter of a convex plane curve Lipschitz with respect to the Hausdorff distance?

answered Oct 4, 2019 at 18:53

4 votes

Does there exist a real-valued function on the hyperbolic plane which has bounded hessian norm and unbounded gradient norm?

answered Apr 22, 2020 at 1:43

4 votes

Accepted

Measure of the boundary of Alexandrov space

answered Nov 18, 2019 at 1:50

4 votes

Accepted

Volume ratio of complete flat manifolds

answered Feb 1, 2020 at 1:48

4 votes

Distance function on a curve on a manifold

answered Jun 10, 2017 at 16:19

4 votes

What is the geometric meaning of one Riemannian metric bigger than the other one on a smooth manifold?

answered Nov 30, 2018 at 18:09

4 votes

Totally geodesic submanifold of codimension 1

answered Sep 2, 2018 at 15:54

4 votes

Accepted

Is every metric continuum almost path-connected?

answered Aug 16, 2018 at 18:18

4 votes

Gromov-Hausdroff convergence for Alexandrov spaces

answered Oct 28, 2015 at 11:42

4 votes

Accepted

Self-avoiding/reflecting geodesics on a convex surface

answered Oct 25, 2015 at 15:03

4 votes

Equality of triangles in normed spaces

answered Sep 30, 2015 at 12:50

4 votes

$|\exp_p(x)\exp_q(T(x))|$ controlled by $|pq|?$ $T$ is parallel transportation in Alexandrov space

answered Oct 30, 2015 at 15:16

4 votes

A clarification on pointed Gromov-Hausdorff convergence

answered May 23, 2016 at 12:37

4 votes

Accepted

Can a nowhere differentiable function preserve measurability?

answered May 26, 2016 at 8:36

4 votes

Geometry of convex subsets in Alexandrov space/ Riemannian manifold

answered Nov 10, 2015 at 16:19

4 votes

Accepted

Wild half-line in a Euclidean space

answered Jan 25, 2016 at 20:01

4 votes

Accepted

Curvature and intersection of submanifolds

answered Nov 7, 2016 at 18:48

4 votes

Accepted

Does every smooth manifold admit a metric with bounded geometry and uniform growth?

answered Jul 19, 2016 at 21:23

4 votes

Accepted

Characterizing surface area

answered Apr 11, 2016 at 20:49

4 votes

Curvature of singular Riemannian metric

answered Sep 8, 2016 at 14:14

4 votes

Accepted

Problem on distances in a polygon

answered Apr 7, 2017 at 17:20

4 votes

Accepted

A non-Finsler metric on $\mathbb{R}^2$

answered Dec 17, 2023 at 23:00

4 votes

Accepted

How to estimate the distance between geodesics and points for Riemannian manifold with positive sectional curvature

answered Jan 1 at 5:34

4 votes

Accepted

Osculating sphere at point of maximal curvature lies to one side

answered Jan 23 at 3:28

4 votes

$2\mathrm{d}$ area maximizing short embeddings

answered Oct 18, 2022 at 21:43

4 votes

Is this projection on the boundary of a convex Lipschitz?

answered Jul 19, 2022 at 14:01

4 votes

Accepted

Partitioning a smooth manifold into geodesically convex sets

answered Sep 22, 2022 at 13:17

4 votes

Can we make distances in a finite subset of a manifold whatever we want?

answered Mar 11, 2022 at 0:21

4 votes

Accepted

Is a cap an Alexandrov space?

answered Dec 2, 2021 at 18:02

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576 Answers

Is there a coordinate-free proof of the hamiltonian character of the geodesic flow?

Is the barycenter of a convex plane curve Lipschitz with respect to the Hausdorff distance?

Does there exist a real-valued function on the hyperbolic plane which has bounded hessian norm and unbounded gradient norm?

Measure of the boundary of Alexandrov space

Volume ratio of complete flat manifolds

Distance function on a curve on a manifold

What is the geometric meaning of one Riemannian metric bigger than the other one on a smooth manifold?

Totally geodesic submanifold of codimension 1

Is every metric continuum almost path-connected?

Gromov-Hausdroff convergence for Alexandrov spaces

Self-avoiding/reflecting geodesics on a convex surface

Equality of triangles in normed spaces

$|\exp_p(x)\exp_q(T(x))|$ controlled by $|pq|?$ $T$ is parallel transportation in Alexandrov space

A clarification on pointed Gromov-Hausdorff convergence

Can a nowhere differentiable function preserve measurability?

Geometry of convex subsets in Alexandrov space/ Riemannian manifold

Wild half-line in a Euclidean space

Curvature and intersection of submanifolds

Does every smooth manifold admit a metric with bounded geometry and uniform growth?

Characterizing surface area

Curvature of singular Riemannian metric

Problem on distances in a polygon

A non-Finsler metric on $\mathbb{R}^2$

How to estimate the distance between geodesics and points for Riemannian manifold with positive sectional curvature

Osculating sphere at point of maximal curvature lies to one side

$2\mathrm{d}$ area maximizing short embeddings

Is this projection on the boundary of a convex Lipschitz?

Partitioning a smooth manifold into geodesically convex sets

Can we make distances in a finite subset of a manifold whatever we want?

Is a cap an Alexandrov space?