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Collection Not Only Scalar Curvature Seminar

00:00:00 / 00:00:00
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Harmonic maps to metric spaces and applications

Harmonic maps are critical points for the energy and existence and compactness results for harmonic maps have played a major role in the advancement of geometric analysis. Gromov-Schoen and Korevaar-Schoen developed a theory of harmonic maps into metric spaces with non-positive curvature in order to address rigidity problems in geometric group theory. In this talk we consider harmonic maps into metric spaces with upper curvature bounds. We will define these objects, state some key results, and highlight their application to rigidity and uniformization problems. We finish the talk by discussing some recently determined Bochner inequalities for maps from (possibly) singular domains.

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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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