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[Lecture] A Generalization of the Geroch Conjecture with Arbitrary Ends
May. 10, 2023

Speaker: Shuli Chen (Stanford University)

Time: 9:00-10:00 a.m., May 10, 2023, GMT+8

Venue: Zoom Meeting ID: 839 1359 1420 Passcode: 051649


The Geroch conjecture (proven by Schoen-Yau and Gromov-Lawson) says that the torus T^n does not admit a metric of positive scalar curvature. In this talk, I will explain how to generalize it to some non-compact settings using μ-bubbles. In particular, I will talk about why the connected sum of a Schoen-Yau-Schick n-manifold with an arbitrary n-manifold does not admit a complete metric of positive scalar curvature for n <=7; this generalizes work of Chodosh and Li. I will also discuss about how to generalize Brendle-Hirsch-Johne’s non-existence result for metrics of positive m-intermediate curvature on N^n = M^{n-m} x T^m to to manifolds with arbitrary ends for n <= 7 and certain m. Here, m-intermediate curvature is a new notion of curvature interpolating between Ricci and scalar curvature.

Shuli Chen is currently a graduate student at Stanford University under the supervision of Otis Chodosh. Her research focuses on minimal surfaces and scalar curvature.

Source: School of Mathematical Sciences