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3 votes
1 answer
135 views

Geodesic convexity of Dirichlet Fundamental Domains

My question is motivated by this question, and this answer to it. Below, let's consider the setup in that answer: Let $M$ be a Riemannian manifold. Let $G\times M\to M$ be a proper action of a ...
13 votes
3 answers
851 views

Are negatively pinched manifold locally conformally flat?

One knows that hyperbolic manifolds are locally conformally flat. How about those negatively pinched manifolds, i.e. the sectional curvature $K$ satisfy: $$ -\Lambda \le K \le -\lambda$$ for $\Lambda&...
0 votes
1 answer
251 views

altering curvature on a tessellation representation of a compact surface

I have been reading about tessellation representations of compact surfaces, such as how the square tiling the plane represents the torus. For surfaces of genus > 1 (the ones that interest me), we ...