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Results tagged with dg.differential-geometry
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user 9152
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
1
answer
102
views
Analytic approximation of the intrinsic distance to the boundary of an open subset
Let $\Omega$ be an open subset of $\mathbb{R}^n$, do we have for any $x\in \Omega$ :
$$\sup_\{\phi\in D(\Omega), \|d\phi\| \le 1\} |\phi(x)|=d_\Omega (x, \partial\Omega),$$
where the norm is the sup …
- 32.4k
2
votes
1
answer
258
views
Tangential behavior of Riemannian exponential
I wonder if the following holds in an arbitrary Riemannian manifold $M$:
assume $x\in M$, $h\in T_x M$, do we have for $u\in T_x M$ exponentiable (if necessary of small enough norm) that:
$$\lim_{t\ …
- 32.4k