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# Collection Not Only Scalar Curvature Seminar

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## Sequences of manifolds with lower bounds on their scalar curvature

If one has a weakly converging sequence of manifolds with a uniform lower bound on their scalar curvature, what properties of scalar curvature persist on the limit space? What additional hypotheses might be added to provide stronger controls on the limit space? What hypotheses are required to be guaranteed that a sequence has a converging subsequence? What notions of convergence might we consider? I will present examples and conjectures.

### Bibliography

• Christina Sormani, Conjectures on Convergence and Scalar Curvature, preprint [arXiv:2103.10093]{https://arxiv.org/abs/2103.10093}

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• 46:29
published on February 3, 2022

## Invitation to scalar curvature

By Mikhail Gromov

01:02:05
published on February 3, 2022

## Scalar and mean curvature comparison via the Dirac operator

By Rudolf Zeidler

49:31
published on February 25, 2022

## Sequences of manifolds with lower bounds on their scalar curvature

By Christina Sormani

51:51
published on February 25, 2022

## Scalar curvature and the dihedral rigidity conjecture

By Chao Li

49:38
published on February 22, 2022

## Some introductory remarks on the Novikov conjecture

By Shmuel Weinberger

59:45
published on February 22, 2022

## The Novikov conjecture and scalar curvature

By Guoliang Yu

54:54
published on March 11, 2022

## Rigidity theorems for the diffeomorphism action on spaces of metrics of positive scalar curvature

By Johannes Ebert

44:46
published on March 11, 2022

## Surgery, bordism and scalar curvature

By Bernhard Hanke

47:18
published on March 25, 2022

## Ricci flow and singularities

By Natasa Sesum

52:49
published on March 25, 2022

## Lower scalar curvature bounds for $C^0$ metrics: a Ricci flow approach

By Paula Burkhardt-Guim

59:42
published on April 7, 2022

## Gromov’s dihedral rigidity conjecture and index theory on manifolds with corners

By Jinming Wang

01:01:04
published on April 7, 2022

## Comparison of scalar curvature, mean curvature and dihedral angles, and their applications

By Zhizhang Xie

45:07
published on April 19, 2022

## Deformations of Dirac operators

By Weiping Zhang

43:37
published on April 21, 2022

## Nonnegative scalar curvature and area decreasing maps on complete foliated manifolds

By Guangxiang Su

44:57
published on May 3, 2022

## Quasi-local mass and geometry of scalar curvature

By Yuguang Shi

01:03:49
published on May 3, 2022

## Incompressible hypersurface, positive scalar curvature and positive mass theorem

By Jintian Zhu

43:08
published on May 11, 2022

## Boundary value problems for Dirac operators

By Christian Bär

01:04:17
published on May 11, 2022

## Distance estimates in the spin setting and the positive mass theorem

By Simone Cecchini

48:01
published on May 24, 2022

## Yamabe constants, Yamabe invariants, and Gromov-Lawson surgeries

By Bernd Ammann

01:10:21
published on May 24, 2022

## Yamabe invariants, Weyl curvature, and the differential topology of 4-manifolds

By Claude LeBrun

47:01
published on June 30, 2022

## Harmonic maps to metric spaces and applications

By Christine Breiner

47:22
published on June 30, 2022

## Level set methods for scalar curvature on three-manifolds

By Daniel Stern

59:15
published on November 14, 2022

## Capacity in low regularity, with connections to general relativity

By Jeff Jauregui

47:02
published on November 3, 2022

## Recent inequalities on the mass-to-capacity ratio

By Pengzi Miao

45:55
published on November 17, 2022

## Scalar curvature rigidity and extremality in dimension 4

By Renato Bettiol

47:42
published on November 17, 2022

## Scalar curvature rigidity

By Thomas Schick

52:09
published on December 30, 2022

## Lipschitz constant and degree of mappings

By Larry Guth

57:53
published on December 30, 2022

## Self-similar solutions to extension and approximation problems

By Robert Young

55:22
published on February 10, 2023

## Currents on metric spaces and intrinsic flat convergence

By Christina Sormani

01:00:01
published on February 10, 2023

## Spherical Plateau problem and applications

By Antoine Song

47:01
published on February 21, 2023

## Recent developments in constant mean curvature hypersurfaces I

By Xin Zhou

51:23
published on February 21, 2023

## Recent developments in constant mean curvature hypersurfaces II

By Liam Mazurowski

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