Curtis Pro

activity

20112020

collaborators

8 papers

math.DG2020

On Delaunay Triangulations of Gromov Sets

Curtis Pro, Frederick Wilhelm

Let $Y$ be a subset of a metric space $X .$ We say that $Y$ is $η$ -Gromov provided $Y$ is $η$ -separated and not properly contained in any other $η$ -separated subset of $X .$ In this…

math.DG2020

Stability, Finiteness and Dimension Four

Curtis Pro, Frederick Wilhelm

We prove that for any $k \in R,$ $v > 0,$ and $D > 0$ there are only finitely many diffeomorphism types of closed Riemannian $4$ -manifolds with sectional curvature $\geq k,$ vo…

math.DG2016

Crosscap Stability

Curtis Pro, Michael Sill, Frederick Wilhelm

We provide an alternative proof that Crosscaps are diffeomorphically stable.

math.DG2016

Diffeomorphism Stability and Codimension Three

Curtis Pro, Frederick Wilhelm

Given $k \in R,$ $v,$ $D > 0,$ and $n \in N,$ let ${M_{α}}_{α = 1}^{\infty}$ be a Gromov-Hausdorff convergent sequence of Riemannian $n$ --manifolds with…

math.DG2014

Sagitta, Lenses, and Maximal Volume

Curtis Pro

We give a characterization of critical points that allows us to define a metric invariant on all Riemannian manifolds $M$ with a lower sectional curvature bound and an upper radius…

math.DG2012

Riemannian Submersions Need Not Preserve Positive Ricci Curvature

Curtis Pro, Frederick Wilhelm

If $π : M \to B$ is a Riemannian Submersion and $M$ has positive sectional curvature, O'Neill's Horizontal Curvature Equation shows that $B$ must also have positive curvature.…

math.DG2012

The Diffeomorphism Type of Manifolds with Almost Maximal Volume

Curtis Pro, Michael Sill, Frederick Wilhelm

The smallest $r$ so that a metric $r$ -ball covers a metric space $M$ is called the radius of $M$ . The volume of a metric $r$ -ball in the space form of constant curvature $k$ is an…

math.DG2011

Flats and Submersions in Non-Negative Curvature

Curtis Pro, Frederick Wilhelm

We find constraints on the extent to which O'Neill's horizontal curvature equation can be used to create positive curvature on the base space of a Riemannian submersion. In particu…