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Featured researches published by Frederick Wilhelm.


Geometry & Topology | 1999

Examples of Riemannian manifolds with positive curvature almost everywhere

Peter Petersen; Frederick Wilhelm

We show that the unit tangent bundle of S 4 and a real cohomology CP 3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not also known to admit positive curvature.


Journal of Geometric Analysis | 2001

An exotic sphere with positive curvature almost everywhere

Frederick Wilhelm

In this article we show that there is an exotic sphere with positive sectional curvature almost everywhere.In 1974 Gromoll and Meyer found a metric of nonnegative sectional on an exotic 7-sphere. They showed that the metric has positive curvature at a point and asserted, without proof, that the metric has positive sectional curvature almost everywhere [4]. We will show here that this assertion is wrong. In fact, the Gromoll-Meyer sphere has zero curvatures on an open set of points. Never the less, its metric can be perturbed to one that has positive curvature almost everywhere.


Geometry & Topology | 2015

How to lift positive Ricci curvature

Catherine Searle; Frederick Wilhelm

Remark Various definitions of lower Ricci curvature bounds on metric spaces are proposed in Kuwae and Shioya [23], Lott and Villani [25], Ohta [28], Sturm [40; 41] and Zhang and Zhu [50]. Our proof only requires that the quotient space of the principal orbits, M reg=G , has Ricci curvature greater than or equal to 1, and since M reg=G is a Riemannian manifold, it does not matter which definition we choose.


Canadian Mathematical Bulletin | 2003

On Frankel's Theorem

Peter Petersen; Frederick Wilhelm

In this paper we show that two minimal hypersurfaces in a manifold with positive Ricci curvature must intersect. This is then generalized to show that in manifolds with positive Ricci cur- vature in the integral sense two minimal hypersurfaces must be close to each other. We also show what happens if a manifold with nonnegative Ricci curvature admits two nonintersecting minimal hypersurfaces.


Proceedings of The London Mathematical Society | 2018

Focal Radius, Rigidity, and Lower Curvature Bounds

Luis Guijarro; Frederick Wilhelm

“This is the accepted version of the following article: Luis Guijarro and Frederick Wilhelm, Focal radius, rigidity, and lower curvature bounds, which has been published in final form at: https://doi.org/10.1112/plms.12113.”


Proceedings of the American Mathematical Society | 2002

The diffeomorphism type of certain ³-bundles over ⁴

Marc Sanchez; Frederick Wilhelm

In this note we show that the unit tangent bundle of S 4 is diffeomorphic to the total space of a certain principal S 3 -bundle over S 4 , solving a problem of James and Whitehead.


arXiv: Differential Geometry | 2008

An exotic sphere with positive sectional curvature

Peter Petersen; Frederick Wilhelm


Journal of Geometric Analysis | 2001

Exotic spheres with lots of positive curvatures

Frederick Wilhelm


arXiv: Differential Geometry | 2014

Riemannian submersions need not preserve positive Ricci curvature

Curtis Pro; Frederick Wilhelm


Differential Geometry and Its Applications | 2012

Infinity-harmonic maps and morphisms

Ye-Lin Ou; Tiffany Troutman; Frederick Wilhelm

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Curtis Pro

University of California

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Peter Petersen

University of California

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Priyanka Rajan

University of California

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Luis Guijarro

Autonomous University of Madrid

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Catherine Searle

National Autonomous University of Mexico

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Thomas Murphy

Université libre de Bruxelles

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Curtis Pro

University of California

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