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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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\ …
Truly's user avatar
  • 205
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 …
Truly's user avatar
  • 205