User Asaf Shachar

24 votes

1 answer

2k views

Geometric interpretation of Hölder's inequality

asked Mar 14, 2018 at 11:28

20 votes

2 answers

1k views

Is the AM-GM inequality the only obstruction for getting a specific sum and product?

real-analysis polynomials systems-of-equations a.m.-g.m.-inequality

asked May 3, 2020 at 9:27

19 votes

3 answers

1k views

If two Riemannian manifolds can be isometrically immersed in each other, are they isometric?

differential-geometry riemannian-geometry smooth-manifolds isometry

asked Nov 1, 2016 at 22:16

18 votes

1 answer

2k views

Is there an explicit left invariant metric on the general linear group?

metric-spaces lie-groups symmetry metric-geometry

asked Feb 13, 2016 at 18:25

18 votes

2 answers

2k views

Can every Riemannian manifold be embedded in a sphere?

riemannian-geometry

asked May 18, 2016 at 20:34

16 votes

3 answers

1k views

Must a matrix of which all conjugates have zero diagonal be zero?

linear-algebra matrices matrix-equations matrix-calculus

asked May 29, 2018 at 11:46

15 votes

2 answers

607 views

Isometry group of a norm is always contained in some Isometry group of an inner product?

linear-algebra normed-spaces inner-products isometry metric-geometry

asked Jun 14, 2015 at 12:03

15 votes

2 answers

2k views

Is every topological manifold completely metrizable?

general-topology manifolds

asked Aug 5, 2015 at 15:46

14 votes

1 answer

3k views

Uniqueness of bi-invariant metrics on Lie groups?

lie-groups riemannian-geometry

asked Jun 10, 2015 at 10:51

13 votes

2 answers

986 views

Metric Isometry is always smooth?

metric-spaces riemannian-geometry smooth-manifolds metric-geometry

asked Aug 10, 2015 at 13:58

13 votes

0 answers

325 views

Non-trivial isometries of the left invariant metric on $GL_n$

lie-groups riemannian-geometry matrix-calculus symmetry isometry

asked Apr 9, 2016 at 10:34

13 votes

1 answer

737 views

Is a general smooth rescaling of a complete vector field itself complete?

differential-geometry partial-differential-equations differential-topology smooth-manifolds vector-fields

asked Jan 15, 2016 at 15:06

13 votes

0 answers

272 views

Is there a volume-preserving diffeomorphism of the disk with prescribed singular values?

multivariable-calculus differential-geometry riemannian-geometry ergodic-theory svd

asked Feb 2, 2020 at 6:49

13 votes

1 answer

406 views

Is every geodesic-preserving diffeomorphism an isometry?

differential-geometry riemannian-geometry symmetry isometry geodesic

asked Nov 6, 2020 at 20:05

12 votes

1 answer

248 views

Is there a "global" convexity locally around a minimum?

real-analysis calculus probability convex-analysis solution-verification

asked Jun 18, 2020 at 9:02

12 votes

1 answer

295 views

Can we recover all matrix minors from some of them?

linear-algebra matrices algebraic-geometry determinant exterior-algebra

asked Jun 26, 2019 at 8:49

12 votes

1 answer

228 views

What is the "right" extra information needed to define the trace of a map between two different vector spaces?

linear-algebra abstract-algebra soft-question category-theory trace

asked Aug 24, 2018 at 13:13

12 votes

1 answer

1k views

"Lebesgue" measurabillity on Riemannian manifolds

real-analysis measure-theory lebesgue-measure smooth-manifolds

asked Aug 27, 2016 at 14:00

12 votes

2 answers

2k views

Distance of a matrix from the orthogonal group

linear-algebra matrices metric-spaces inner-products

asked Oct 13, 2015 at 8:35

11 votes

0 answers

734 views

Every vector bundle has a metric connection?

differential-geometry vector-bundles connections

asked Oct 1, 2015 at 22:01

11 votes

1 answer

1k views

Does Hodge-star commute with metric connections?

differential-geometry riemannian-geometry vector-bundles connections

asked Nov 2, 2016 at 18:40

11 votes

1 answer

326 views

The image of every strictly non-expanding map between spheres is contained in an open hemisphere?

geometry lipschitz-functions convex-geometry convex-hulls contraction-operator

asked Mar 3, 2017 at 15:08

11 votes

7 answers

757 views

The vertices of a tetrahedron lie on a sphere

soft-question euclidean-geometry symmetry spherical-geometry platonic-solids

asked Apr 26 at 18:34

10 votes

2 answers

296 views

"Universal" differential identities

abstract-algebra differential-operators universal-property congruence-relations

asked May 11, 2017 at 13:28

10 votes

1 answer

655 views

Solutions to Dirichlet problem on manifolds with boundary

reference-request riemannian-geometry smooth-manifolds harmonic-functions

asked Aug 22, 2015 at 20:01

10 votes

3 answers

640 views

The Riemannian Distance function does not change if we use smooth paths?

riemannian-geometry smooth-manifolds

asked Jul 30, 2015 at 13:47

10 votes

0 answers

165 views

Does the space of matrices above rank $k$ admit a transitive Lie group action?

linear-algebra lie-groups group-actions matrix-rank homogeneous-spaces

asked Jun 18, 2018 at 6:32

10 votes

2 answers

308 views

Is this identity about the Ricci curvature true?

differential-geometry reference-request riemannian-geometry curvature trace

asked Dec 10, 2017 at 7:08

10 votes

1 answer

184 views

Can we approximate a.e. invertible matrices with everywhere invertible matrices in $L^2$ sense?

real-analysis measure-theory determinant lp-spaces perturbation-theory

asked May 24, 2019 at 6:23

10 votes

1 answer

250 views

Are gradient flows the quickest way to minimize a function for a short time?

multivariable-calculus differential-geometry optimization gradient-descent gradient-flows

asked Oct 5, 2019 at 12:33

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791 Questions

Geometric interpretation of Hölder's inequality

Is the AM-GM inequality the only obstruction for getting a specific sum and product?

If two Riemannian manifolds can be isometrically immersed in each other, are they isometric?

Is there an explicit left invariant metric on the general linear group?

Can every Riemannian manifold be embedded in a sphere?

Must a matrix of which all conjugates have zero diagonal be zero?

Isometry group of a norm is always contained in some Isometry group of an inner product?

Is every topological manifold completely metrizable?

Uniqueness of bi-invariant metrics on Lie groups?

Metric Isometry is always smooth?

Non-trivial isometries of the left invariant metric on $GL_n$

Is a general smooth rescaling of a complete vector field itself complete?

Is there a volume-preserving diffeomorphism of the disk with prescribed singular values?

Is every geodesic-preserving diffeomorphism an isometry?

Is there a "global" convexity locally around a minimum?

Can we recover all matrix minors from some of them?

What is the "right" extra information needed to define the trace of a map between two different vector spaces?

"Lebesgue" measurabillity on Riemannian manifolds

Distance of a matrix from the orthogonal group

Every vector bundle has a metric connection?

Does Hodge-star commute with metric connections?

The image of every strictly non-expanding map between spheres is contained in an open hemisphere?

The vertices of a tetrahedron lie on a sphere

"Universal" differential identities

Solutions to Dirichlet problem on manifolds with boundary

The Riemannian Distance function does not change if we use smooth paths?

Does the space of matrices above rank $k$ admit a transitive Lie group action?

Is this identity about the Ricci curvature true?

Can we approximate a.e. invertible matrices with everywhere invertible matrices in $L^2$ sense?

Are gradient flows the quickest way to minimize a function for a short time?