User Mohammad Ghomi

80 votes

1 answer

3k views

Converse to Euclid's fifth postulate

asked Oct 14, 2017 at 15:04

38 votes

0 answers

1k views

Converse of the Archimedean property of the sphere

asked Oct 9, 2017 at 22:01

29 votes

2 answers

2k views

Contractibility of the space of Jordan curves

asked Jun 16, 2023 at 19:20

23 votes

1 answer

714 views

Covering the unit sphere in $\mathbf{R}^n$ with $2n$ congruent disks

asked Aug 28, 2022 at 22:37

22 votes

3 answers

1k views

Equilaterally triangulated surfaces with prescribed boundary

asked Oct 20, 2017 at 3:16

13 votes

2 answers

872 views

Intrinsic vs Extrinsic geometry of convex surfaces

asked Oct 16, 2017 at 0:55

12 votes

1 answer

281 views

Rigidity of doubled convex caps

asked Apr 16, 2018 at 20:17

11 votes

1 answer

940 views

Equivariant sections of fiber bundles

asked Nov 25, 2017 at 21:34

10 votes

0 answers

265 views

Plank invariant measures on convex bodies

asked Oct 13, 2017 at 1:43

9 votes

1 answer

429 views

Perturbing metrics with nonpositive curvature

asked May 20, 2022 at 21:41

8 votes

2 answers

490 views

Continuous point map for spherical domains

asked Jul 13, 2023 at 23:49

7 votes

3 answers

705 views

A continuous version of Carathéodory's convex hull theorem

asked Feb 28 at 19:59

7 votes

2 answers

360 views

Cone unfolding of space curves

asked Nov 1, 2020 at 16:28

6 votes

1 answer

254 views

Triangulations of convex surfaces

asked May 12, 2018 at 14:50

6 votes

2 answers

377 views

Convex surfaces with minimal total curvature in Cartan-Hadamard 3-space

asked Jun 3, 2022 at 3:57

6 votes

3 answers

561 views

Smale's theorem for $C^1$ diffeomorphisms of the sphere

asked Nov 29, 2017 at 14:24

5 votes

2 answers

294 views

Convex caps with prescribed edges

asked Sep 21, 2017 at 2:30

5 votes

1 answer

333 views

Manifolds with nonpositive radial curvature

asked Apr 20, 2022 at 18:56

4 votes

1 answer

193 views

Approximate isometric embeddings of surfaces

asked May 9, 2023 at 0:55

4 votes

1 answer

124 views

Convex caps with prescribed edges and curvature

asked Oct 12, 2017 at 2:35

4 votes

1 answer

187 views

Convex hull of 3 points in Cartan-Hadamard manifolds

asked Nov 23, 2023 at 17:47

3 votes

1 answer

257 views

Asymptotic parametrization for negatively curved surfaces

asked Nov 12 at 17:58

1 vote

0 answers

99 views

Shortest loop through vertices of a convex polytope

asked Oct 10 at 20:08

1 vote

2 answers

231 views

A triangle comparison in CAT(0) spaces

asked Jan 30 at 20:17

1 vote

0 answers

107 views

Planar sections of convex sets in Cartan-Hadamard manifolds

asked Oct 28, 2023 at 16:17

1 vote

0 answers

126 views

What is an umbilic point of a convex polyhedron?

asked Oct 16, 2017 at 20:31

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26 Questions

Converse to Euclid's fifth postulate

Converse of the Archimedean property of the sphere

Contractibility of the space of Jordan curves

Covering the unit sphere in $\mathbf{R}^n$ with $2n$ congruent disks

Equilaterally triangulated surfaces with prescribed boundary

Intrinsic vs Extrinsic geometry of convex surfaces

Rigidity of doubled convex caps

Equivariant sections of fiber bundles

Plank invariant measures on convex bodies

Perturbing metrics with nonpositive curvature

Continuous point map for spherical domains

A continuous version of Carathéodory's convex hull theorem

Cone unfolding of space curves

Triangulations of convex surfaces

Convex surfaces with minimal total curvature in Cartan-Hadamard 3-space

Smale's theorem for $C^1$ diffeomorphisms of the sphere

Convex caps with prescribed edges

Manifolds with nonpositive radial curvature

Approximate isometric embeddings of surfaces

Convex caps with prescribed edges and curvature

Convex hull of 3 points in Cartan-Hadamard manifolds

Asymptotic parametrization for negatively curved surfaces

Shortest loop through vertices of a convex polytope

A triangle comparison in CAT(0) spaces

Planar sections of convex sets in Cartan-Hadamard manifolds

What is an umbilic point of a convex polyhedron?