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Results tagged with dg.differential-geometry
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user 127309
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
10
votes
Volume of manifolds embedded in $\mathbb{R}^n$
Yes if $N$ is convex - the flow will even increase or decrease distances. No if not convex, looking at $n=2$. The curve length of those parts of $N$ that are concave with respect to $X$ will decrease, …
- 271
7
votes
Accepted
Holonomy bounded in terms of area and the curvature
There are in fact more precise versions, expressing the parallel translation around a loop as the identity map plus a curvature integral over a homotopy. References:
Section 3.1 of Werner Ballmann's l …
- 271
4
votes
The existence of length-minimizing path between two points in a Riemannian manifold with bou...
Alexander, Berg, Bishop: The Riemannian obstacle problem. https://projecteuclid.org/download/pdf_1/euclid.ijm/1255989406
- 271
2
votes
Groups of conformal isomorphisms of simply connected surfaces
After postcomposing with a suitable Möbius transformation one can assume that f maps infinity to infinity. So f is an entire function on the complex plane. By Casorati-Weierstrass (or Picard), it cann …
- 271