User Jialong Deng

36 votes

1 answer

2k views

Can a topological manifold have different tangent bundles?

asked Apr 18, 2016 at 14:41

14 votes

0 answers

579 views

Aspherical manifold and non-positive curvature

asked Oct 26, 2016 at 14:11

11 votes

1 answer

780 views

Can the diameter be controled by the injectivity radius and the volume?

asked Nov 24, 2019 at 13:02

11 votes

1 answer

442 views

Scalar curvature and the degree of symmetry

asked Jul 29, 2021 at 14:24

9 votes

2 answers

385 views

Does positive scalar curvature imply vanishing of the simplicial volume on a closed Riemannian manifold?

asked Oct 22, 2019 at 8:29

7 votes

0 answers

347 views

Have examples of non-simple connected higher-dimensions integer homology sphere?

asked Aug 14, 2016 at 13:15

7 votes

1 answer

259 views

Can we realize the smooth metric of an Alexandrov space with nonnegative curvature by a Riemannian structure?

asked Mar 6, 2017 at 14:53

7 votes

1 answer

281 views

Existence of harmonic maps onto the $n$-sphere

asked May 11, 2021 at 19:10

6 votes

0 answers

135 views

How to decide a closed Top/PL manifold is a boundary?

asked Oct 20, 2017 at 14:02

6 votes

2 answers

412 views

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

asked Nov 30, 2018 at 13:32

6 votes

1 answer

452 views

When the image of a convex set in $\mathbb{R}^n$ is still a convex set?

asked May 27, 2019 at 14:51

5 votes

1 answer

251 views

If M times circle admits a locally CAT(0)-metric, then M also carries a locally CAT(0)-metric?

asked Jul 30, 2019 at 18:27

5 votes

1 answer

739 views

The product of two Hausdorff measures

asked Dec 20, 2020 at 13:54

5 votes

3 answers

359 views

Recovering the length metric from Hausdorff measure

asked May 1, 2021 at 12:32

5 votes

0 answers

51 views

The universal cover and embedding

asked Mar 14 at 6:29

3 votes

0 answers

51 views

Harmonic map in the homotopy class of the identity map

asked Dec 8 at 16:20

3 votes

0 answers

93 views

What can be reflected by the $C^0$-limit of Riemannian metrics?

asked Dec 2, 2019 at 6:02

3 votes

0 answers

214 views

If the total space of circle bundle over hyperbolic manifold admits Riemannain metric of non-positive sectional curvature?

asked Dec 17, 2018 at 13:23

3 votes

0 answers

228 views

From nonnegative sectional curvature to positive sectional curvature

asked Mar 8, 2017 at 15:06

3 votes

0 answers

144 views

Can we use the "size" of smooth structure set to predict the information geometry or other topological information?

asked Apr 23, 2016 at 15:48

2 votes

1 answer

313 views

Non-negatively curved manifolds and the volume of balls

asked Apr 10, 2022 at 13:45

1 vote

0 answers

342 views

What is the meaning of Conjugate radius and Injectivity radius?

asked Mar 5, 2019 at 20:18

1 vote

1 answer

249 views

Non-positive sectional curvature in 3-dimensional manifold

asked Oct 19, 2019 at 9:25

0 votes

1 answer

683 views

The properties of total variation metric

asked Jun 11, 2020 at 7:34

Stack Exchange Network

24 Questions

Can a topological manifold have different tangent bundles?

Aspherical manifold and non-positive curvature

Can the diameter be controled by the injectivity radius and the volume?

Scalar curvature and the degree of symmetry

Does positive scalar curvature imply vanishing of the simplicial volume on a closed Riemannian manifold?

Have examples of non-simple connected higher-dimensions integer homology sphere?

Can we realize the smooth metric of an Alexandrov space with nonnegative curvature by a Riemannian structure?

Existence of harmonic maps onto the $n$-sphere

How to decide a closed Top/PL manifold is a boundary?

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

When the image of a convex set in $\mathbb{R}^n$ is still a convex set?

If M times circle admits a locally CAT(0)-metric, then M also carries a locally CAT(0)-metric?

The product of two Hausdorff measures

Recovering the length metric from Hausdorff measure

The universal cover and embedding

Harmonic map in the homotopy class of the identity map

What can be reflected by the $C^0$-limit of Riemannian metrics?

If the total space of circle bundle over hyperbolic manifold admits Riemannain metric of non-positive sectional curvature?

From nonnegative sectional curvature to positive sectional curvature

Can we use the "size" of smooth structure set to predict the information geometry or other topological information?

Non-negatively curved manifolds and the volume of balls

What is the meaning of Conjugate radius and Injectivity radius?

Non-positive sectional curvature in 3-dimensional manifold

The properties of total variation metric