Question

Making intuition rigorous that integral of some positive function on set should be monotone in the Haar measure of the set

score 61 · Answer 1 · 2026-03-25 14:24:34

61

Views

Making intuition rigorous that integral of some positive function on set should be monotone in the Haar measure of the set

Published on 25 Mar 2026 - 14:24

score 40 · Answer 2 · 2026-03-25 14:25:41

40

Views

Is there an example of reducible compact 3-manifold with boundary that has no embedded incompressible two-sided surface?

Published on 25 Mar 2026 - 14:25

score 152 · Answer 3 · 2026-03-25 14:21:50

152

Views

Uniformization theorem for $C^k$ surfaces?

Published on 25 Mar 2026 - 14:21

score 32 · Answer 4 · 2026-04-11 23:07:33

32

Views

integral constraint induce a manifold on Sobolev space

Published on 11 Apr 2026 - 23:07

score 97 · Answer 5 · 2026-04-16 14:04:45

97

Views

Suppose $M$ has trivial 1-st de Rham cohomology group. For which integers $k$ does there exist a smooth map $f : M → T^n$ of degree $k$?

Published on 16 Apr 2026 - 14:04

score 63 · Answer 6 · 2026-04-14 17:05:25

63

Views

Bounding a Sobolev norm on product manifold

Published on 14 Apr 2026 - 17:05

score 151 · Answer 7 · 2026-04-15 22:55:26

151

Views

relationship between $f_\pi:\pi_1(M)\to \pi_1(N)$ and $\deg(f)$

Published on 15 Apr 2026 - 22:55

score 565 · Answer 8 · 2026-04-15 08:03:40

565

Views

Homotopy type of manifolds homeomorphic to the interior of a compact manifold with boundary

Published on 15 Apr 2026 - 8:03

score 90 · Answer 9 · 2026-04-16 13:46:52

90

Views

Necessity of compactness of manifolds $M,N$ for smooth approximation of $W^{1,p}(M,N)$.

Published on 16 Apr 2026 - 13:46

score 3.4k · Answer 10 · 2026-04-14 02:54:59

3.4k

Views

Show that injective immersion of a compact manifold is an embedding

Published on 14 Apr 2026 - 2:54

score 41 · Answer 11 · 2026-04-14 16:45:55

41

Views

Menger compacta and topological joins

Published on 14 Apr 2026 - 16:45

score 709 · Answer 12 · 2026-04-13 03:28:40

709

Views

compact manifold is complete

Published on 13 Apr 2026 - 3:28

score 431 · Answer 13 · 2026-04-16 04:18:50

431

Views

On Poincaré duality and the universal coefficient theorem

Published on 16 Apr 2026 - 4:18

score 98 · Answer 14 · 2026-04-13 02:26:05

98

Views

Can a group G generated by $k$ elements act properly discontinuously freely and cocompactly on $\mathbb{R}^n$, for $n > k$

Published on 13 Apr 2026 - 2:26

score 434 · Answer 15 · 2026-03-25 14:25:30

434

Views

Is the boundary of every 2-manifold the disjoint union of circles?

Published on 25 Mar 2026 - 14:25

List Question

Making intuition rigorous that integral of some positive function on set should be monotone in the Haar measure of the set

Is there an example of reducible compact 3-manifold with boundary that has no embedded incompressible two-sided surface?

Uniformization theorem for $C^k$ surfaces?

integral constraint induce a manifold on Sobolev space

Suppose $M$ has trivial 1-st de Rham cohomology group. For which integers $k$ does there exist a smooth map $f : M → T^n$ of degree $k$?

Bounding a Sobolev norm on product manifold

relationship between $f_\pi:\pi_1(M)\to \pi_1(N)$ and $\deg(f)$

Homotopy type of manifolds homeomorphic to the interior of a compact manifold with boundary

Necessity of compactness of manifolds $M,N$ for smooth approximation of $W^{1,p}(M,N)$.

Show that injective immersion of a compact manifold is an embedding

Menger compacta and topological joins

compact manifold is complete

On Poincaré duality and the universal coefficient theorem

Can a group G generated by $k$ elements act properly discontinuously freely and cocompactly on $\mathbb{R}^n$, for $n > k$

Is the boundary of every 2-manifold the disjoint union of circles?

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