Question

If $π$ is the projection of a surface $M$ onto the 2-sphere $S^2$, then $σ_{S^2}(B)=\int_{π^{-1}(B)}σ_M(dy)\frac{|⟨ν_M(y),π(y)⟩|}{|y|^2}$

score 82 · Answer 1 · 2026-03-25 12:17:52

82

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If $π$ is the projection of a surface $M$ onto the 2-sphere $S^2$, then $σ_{S^2}(B)=\int_{π^{-1}(B)}σ_M(dy)\frac{|⟨ν_M(y),π(y)⟩|}{|y|^2}$

Published on 25 Mar 2026 - 12:17

score 978 · Answer 2 · 2020-01-24 04:52:29

978

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score 672 · Answer 3 · 2026-03-27 16:26:16

672

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145

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score 44 · Answer 5 · 2020-02-01 10:02:57

44

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26

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461

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139

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score 57 · Answer 10 · 2026-03-28 06:01:32

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959

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192

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score 170 · Answer 15 · 2020-02-26 19:47:01

170

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List Question

If $π$ is the projection of a surface $M$ onto the 2-sphere $S^2$, then $σ_{S^2}(B)=\int_{π^{-1}(B)}σ_M(dy)\frac{|⟨ν_M(y),π(y)⟩|}{|y|^2}$

Gradient as normal to a surface

What is the local canonical form of a regular surface?

The out-flux of the vector field $F(x,y,z)=(-sin(2x)+ye^(3z),-(y+1)^2,2z(y+cos(2x)+3)$

How do the fundamental forms change under an image of a diffeomorphism?

What is the name of this geometric shape formed by changing the condition of spheriod formation?

Find the area of $z^2=4-y^2$ between $x =2$ and $x =y$

Mapping from one isometric surface to another

How to prove that two parametrizations of a surface M give the same tangent plane

Classfying quadratic surface $z=x^2+2xy+y^2$.

Equality of Surface area of sphere and Cylinder

Short proof that a surface has constant Gaussian curvature

Prove that the cone given by $σ(u,v) = (\cos(u)v, \sin(u)v, v)$ with $0 < u < 2\pi$ and $0 < v < \infty$ is isometric to (part of) the plane

Curvature of Lobachevsky plane

Find ideal width and height of n same rectangles inside a rectangle

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