Question

Prove that $\int |K|\geq 8\pi$ for a compact surface with genus $>0$

score 855 · Answer 1 · 2026-03-28 11:22:03

855

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Prove that $\int |K|\geq 8\pi$ for a compact surface with genus $>0$

Published on 28 Mar 2026 - 11:22

score 256 · Answer 2 · 2016-09-04 17:18:17

256

Views

Tangent planes of a surface parallel to a fixed direction

Published on 04 Sep 2016 - 17:18

score 42 · Answer 3 · 2016-09-05 22:26:34

42

Views

Interpretation for multivariable functions graphing

Published on 05 Sep 2016 - 22:26

score 262 · Answer 4 · 2026-03-26 08:03:57

262

Views

Non-orientable surface

Published on 26 Mar 2026 - 8:03

score 52 · Answer 5 · 2026-03-28 11:12:36

52

Views

Unlimited connected surface with $K>0$

Published on 28 Mar 2026 - 11:12

score 115 · Answer 6 · 2016-09-06 22:42:30

115

Views

Proving that $S$ is a sphere

Published on 06 Sep 2016 - 22:42

score 1k · Answer 7 · 2016-09-07 13:12:39

1k

Views

Angle plane makes with semi-meridian on sphere

Published on 07 Sep 2016 - 13:12

score 521 · Answer 8 · 2016-09-13 19:26:36

521

Views

The only surface with at least three distinct lines through each of its points is the plane

Published on 13 Sep 2016 - 19:26

score 341 · Answer 9 · 2016-09-16 00:50:54

341

Views

Gaussian curvature is identically zero if $\vec n_u$ and $\vec n_v$ are linearly dependent

Published on 16 Sep 2016 - 0:50

score 492 · Answer 10 · 2026-03-31 10:08:37

492

Views

Surface area and volume where domains are given by inequalities

Published on 31 Mar 2026 - 10:08

score 377 · Answer 11 · 2016-09-23 13:26:56

377

Views

Projecting an $n$-dimensional cube in $n-1$ dimensions

Published on 23 Sep 2016 - 13:26

score 281 · Answer 12 · 2026-03-25 12:54:18

281

Views

Some questions about rigorous proof of cut and paste technique in constructing connected sum

Published on 25 Mar 2026 - 12:54

score 1.7k · Answer 13 · 2016-09-25 14:48:02

1.7k

Views

Find the locus of the vertices of the right circular cones that pass through the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, z=0$

Published on 25 Sep 2016 - 14:48

score 238 · Answer 14 · 2026-03-25 12:52:56

238

Views

$(H^2-K) dA$ is globally invariant under inversions

Published on 25 Mar 2026 - 12:52

score 840 · Answer 15 · 2026-03-30 02:12:01

840

Views

Least square plane fit cubic surface to 3d points

Published on 30 Mar 2026 - 2:12

List Question

Prove that $\int |K|\geq 8\pi$ for a compact surface with genus $>0$

Tangent planes of a surface parallel to a fixed direction

Interpretation for multivariable functions graphing

Non-orientable surface

Unlimited connected surface with $K>0$

Proving that $S$ is a sphere

Angle plane makes with semi-meridian on sphere

The only surface with at least three distinct lines through each of its points is the plane

Gaussian curvature is identically zero if $\vec n_u$ and $\vec n_v$ are linearly dependent

Surface area and volume where domains are given by inequalities

Projecting an $n$-dimensional cube in $n-1$ dimensions

Some questions about rigorous proof of cut and paste technique in constructing connected sum

Find the locus of the vertices of the right circular cones that pass through the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, z=0$

$(H^2-K) dA$ is globally invariant under inversions

Least square plane fit cubic surface to 3d points

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