Question

Characterizing the smooth maps $f : M\to N$ such that $E = \{(x, y)\in M\times M : f(x) = f(y)\}$ is a smooth submanifold of $M\times M$.

score 98 · Answer 1 · 2021-07-13 03:47:34

98

Views

Characterizing the smooth maps $f : M\to N$ such that $E = \{(x, y)\in M\times M : f(x) = f(y)\}$ is a smooth submanifold of $M\times M$.

Published on 13 Jul 2021 - 3:47

score 70 · Answer 2 · 2021-07-20 01:03:40

70

Views

If $M\subseteq H$ is a submanifold diffeomorphic to the 1-sphere $\mathbb{S}^1$, then $\int _M\omega =0$

Published on 20 Jul 2021 - 1:03

score 157 · Answer 3 · 2021-07-27 17:59:21

157

Views

Minmax curvature of surface in $\mathbb{R}^3$

Published on 27 Jul 2021 - 17:59

score 67 · Answer 4 · 2026-03-27 07:17:03

67

Views

Are the compact three-dimensional submanifolds $\mathbb{R}^3$ unions of cubes of the unit Cartesian lattice?

Published on 27 Mar 2026 - 7:17

score 368 · Answer 5 · 2021-08-03 12:11:39

368

Views

Proof of the weak Whitney Embedding theorem

Published on 03 Aug 2021 - 12:11

score 85 · Answer 6 · 2021-08-06 21:26:01

85

Views

Prove that for all $p\in M$ there's an $M$-open set $p\in U\subset M$ and $\varepsilon >0$ such that $(-\varepsilon,\varepsilon)\times U\subset D$

Published on 06 Aug 2021 - 21:26

score 93 · Answer 7 · 2026-03-26 06:02:56

93

Views

Embedded Ricci Flow

Published on 26 Mar 2026 - 6:02

score 161 · Answer 8 · 2021-08-16 10:11:38

161

Views

Representing hypersurfaces as graphs

Published on 16 Aug 2021 - 10:11

score 55 · Answer 9 · 2021-08-18 16:38:48

55

Views

Idea about isometric embedding in two dimension

Published on 18 Aug 2021 - 16:38

score 383 · Answer 10 · 2021-08-23 12:22:24

383

Views

Reference request: Allard's regularity Theorem for smooth submanifolds

Published on 23 Aug 2021 - 12:22

score 62 · Answer 11 · 2021-08-24 12:59:19

62

Views

Definition of unit normal vector in do Carmo

Published on 24 Aug 2021 - 12:59

score 52 · Answer 12 · 2021-08-30 08:03:54

52

Views

General form of fibers of Infinite dimensional manifold distribution

Published on 30 Aug 2021 - 8:03

score 63 · Answer 13 · 2021-08-30 19:12:59

63

Views

Find a submersion $\varphi :U\to \mathbb{R}^{n-m}$ such that $\varphi^{-1}(\{0\})=M$ in which $M\subseteq\mathbb{R}^n$ is smooth submanifold

Published on 30 Aug 2021 - 19:12

score 397 · Answer 14 · 2021-09-02 14:21:18

397

Views

Immersion $(x, y, z)\mapsto (xy, xz, yz)$ from sphere

Published on 02 Sep 2021 - 14:21

score 1.2k · Answer 15 · 2021-09-02 16:44:33

1.2k

Views

Is a figure eight a manifold

Published on 02 Sep 2021 - 16:44

List Question

Characterizing the smooth maps $f : M\to N$ such that $E = \{(x, y)\in M\times M : f(x) = f(y)\}$ is a smooth submanifold of $M\times M$.

If $M\subseteq H$ is a submanifold diffeomorphic to the 1-sphere $\mathbb{S}^1$, then $\int _M\omega =0$

Minmax curvature of surface in $\mathbb{R}^3$

Are the compact three-dimensional submanifolds $\mathbb{R}^3$ unions of cubes of the unit Cartesian lattice?

Proof of the weak Whitney Embedding theorem

Prove that for all $p\in M$ there's an $M$-open set $p\in U\subset M$ and $\varepsilon >0$ such that $(-\varepsilon,\varepsilon)\times U\subset D$

Embedded Ricci Flow

Representing hypersurfaces as graphs

Idea about isometric embedding in two dimension

Reference request: Allard's regularity Theorem for smooth submanifolds

Definition of unit normal vector in do Carmo

General form of fibers of Infinite dimensional manifold distribution

Find a submersion $\varphi :U\to \mathbb{R}^{n-m}$ such that $\varphi^{-1}(\{0\})=M$ in which $M\subseteq\mathbb{R}^n$ is smooth submanifold

Immersion $(x, y, z)\mapsto (xy, xz, yz)$ from sphere

Is a figure eight a manifold

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