Questions tagged [comparison-geometry]

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3
votes
2answers
103 views

Is the radial projection map area increasing?

Let $S$ be a hypersurface enclosed inside the unit sphere in $R^n$. Assume that every ray $\{t x: t \geq 0 \}$ intersects $S$ at most once. Is it always true that ${\rm Area}(S) \leq {\rm Area}(P(S))$...
7
votes
1answer
480 views

Simple application of Bochner--Reilly--Weitzenböck type formulas

I am looking for simple (but not worn-out) application of Bochner--Weitzenböck type formulas in comparison geometry. (I want to use it as a motivation for students.) The vanishing theorems and ...
17
votes
3answers
1k views

On closed simple curve with curvature at most 1

I am looking for the reference to the following theorem. I have to apply a similar statement, and it would be nice to trace the source. Please note, I know few proofs in fact it is Problem 3 in my ...