All Questions

The reach $\tau_M$ of a manifold $M$ is the largest number such that any point at distance less than $\tau_M$ from $M$ has a unique nearest point on $M$. This concept seems quite related to the local ...

Consider the complex upper half plane $\mathbb{H}$ with the hyperbolic geometry. Fix a point $z \in \mathbb{H}$ and also a geodesic $c$. I want to find a hyperbolic translation $\gamma c$ passes that ...

Question: Given a smooth, convex, closed surface. How would one find points on it with the property: the average of the geodesic distances from that point to all other points on the surface (the ...

Let $M$ and $N$ be manifolds and let $T: M \to N$ be a bijective map. Let $ \mathcal{F}(M,\mathbb{R})$ (resp.$ \mathcal{F}(N,\mathbb{R})$) be the space of all functions from $M$ (resp. $N$) to $\...

For a flat plane with certain boundary, e.g., a rectangular patch, is it possible to conformally displace or deform such patch to a curved bump with exact same boundary? In this thesis, Dr. Keenan ...