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Seminar

Geometry: Geometry of smooth manifolds with measure May 11, 2016 (11:00 AM PDT - 12:00 PM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) William Wylie (Syracuse University)
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We introduce an approach to smooth manifolds with measure that takes a  natural torsion free connection as the fundamental object of study.  We obtain new versions of  the  Laplacian and volume comparison theorems which are valid under weaker curvature assumptions than have previously been considered in the literature.   This leads to generalizations of theorems of Myers', Cheng, and Cheeger-Gromoll.  We also study the holonomy of the weighted connection and prove a version of the deRham splitting theorem. This is joint work with Dmytro Yeroshkin of Syracuse. 

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