Frederick Wilhelm

activity

19952020

most citedAn exotic sphere with positive sectional curvature

62 citations · 133 across the 19 of their papers we have counts for

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21 papers · 1 filter

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.DG2018

A softer connectivity principle

Luis Guijarro, Frederick Wilhelm

We give soft, quantitatively optimal extensions of the classical Sphere Theorem, Wilking's connectivity principle and Frankel's Theorem to the context of $k$ -th Ricci curvature.…

math.DG2017

Random Manifolds have no Totally Geodesic Submanifolds

Thomas Murphy, Frederick Wilhelm

For $n \geq 4$ we show that generic closed Riemannian $n$ -manifolds have no nontrivial totally geodesic submanifolds, answering a question of Spivak. An immediate consequence is a s…

math.DG2016

Crosscap Stability

Curtis Pro, Michael Sill, Frederick Wilhelm

We provide an alternative proof that Crosscaps are diffeomorphically stable.

math.DG2016★ 4 cited

Restrictions on Submanifolds via Focal Radius Bounds

Luis Guijarro, Frederick Wilhelm

We give an optimal estimate for the norm of any submanifold's second fundamental form in terms of its focal radius and the lower sectional curvature bound of the ambient manifold.…