Embedded Files
Eduardo Garcia-Rio (Univ. Santiago de Compostela, Spain)
Eduardo Garcia-Rio (Univ. Santiago de Compostela, Spain)
DATE: September 24, 2020, Thursday 2:00 PM
DATE: September 24, 2020, Thursday 2:00 PM
TITLE: Critical metrics for quadratic curvature functionals
TITLE: Critical metrics for quadratic curvature functionals
ABSTRACT: In this talk, I will discuss some recent progress in the study of three- and four-dimensional critical metrics. Special emphasis will be made on the functional given by the L^2-norm of the Weyl curvature tensor in the homogeneous setting, and the existence of metrics with non-constant scalar curvature which are critical for all quadratic curvature functionals.
ABSTRACT: In this talk, I will discuss some recent progress in the study of three- and four-dimensional critical metrics. Special emphasis will be made on the functional given by the L^2-norm of the Weyl curvature tensor in the homogeneous setting, and the existence of metrics with non-constant scalar curvature which are critical for all quadratic curvature functionals.
Xiaodong Cao (Cornell University, USA)
Xiaodong Cao (Cornell University, USA)
DATE: September 17, 2020, Thursday 2:00 PM
DATE: September 17, 2020, Thursday 2:00 PM
TITLE: Some Progress on Four-dimensional Einstein Manifolds
TITLE: Some Progress on Four-dimensional Einstein Manifolds
ABSTRACT: In this talk, I will discuss some recent progress in the study of 4-dimensional Einstein manifolds, and some progress on the geometry of 4-manifolds in general. These are joint work with Hung Tran.
ABSTRACT: In this talk, I will discuss some recent progress in the study of 4-dimensional Einstein manifolds, and some progress on the geometry of 4-manifolds in general. These are joint work with Hung Tran.
Gerhard Huisken (University of Tubingen & Oberwolfach Institute for Mathematics, Germany)
Gerhard Huisken (University of Tubingen & Oberwolfach Institute for Mathematics, Germany)
DATE: September 10, 2020, Thursday 2:00 PM.
DATE: September 10, 2020, Thursday 2:00 PM.
TITLE: Mean curvature flow with surgery
TITLE: Mean curvature flow with surgery
ABSTRACT: The lecture first explains the classification of singularities for mean curvature flow of 2-convex surfaces, that is of hypersurfaces where the sum of any two principal curvatures is positive. The classification and precise description of singularities is the basis of an algorithm that overcomes all singularities with finitely many surgeries and provides longtime solutions that allow topological applications. Differences between the higher dimensional case (joint work with C. Sinestrari) and the 2d-case (joint with S. Brendle) are also explained.
ABSTRACT: The lecture first explains the classification of singularities for mean curvature flow of 2-convex surfaces, that is of hypersurfaces where the sum of any two principal curvatures is positive. The classification and precise description of singularities is the basis of an algorithm that overcomes all singularities with finitely many surgeries and provides longtime solutions that allow topological applications. Differences between the higher dimensional case (joint work with C. Sinestrari) and the 2d-case (joint with S. Brendle) are also explained.
Guofang Wei (University of California, Santa Barbara, USA)
Guofang Wei (University of California, Santa Barbara, USA)
DATE: August 27, 2020, Thursday 2:00 PM.
DATE: August 27, 2020, Thursday 2:00 PM.
TITLE: Ricci flow and L^{n/2}-curvature pinching results
TITLE: Ricci flow and L^{n/2}-curvature pinching results
ABSTRACT: Using Ricci flow we obtain an L^{n/2}-curvature pinching sphere theorem for Yamabe metrics. This generalizes the earlier work of Hebey–Vaugon which requires L^p pinching for p>n/2. We also obtain an L^{n/2} version of Gromov’s almost flat manifolds theorem in the non-collapsing case. This is joined with Eric Chen and Rugang Ye.
ABSTRACT: Using Ricci flow we obtain an L^{n/2}-curvature pinching sphere theorem for Yamabe metrics. This generalizes the earlier work of Hebey–Vaugon which requires L^p pinching for p>n/2. We also obtain an L^{n/2} version of Gromov’s almost flat manifolds theorem in the non-collapsing case. This is joined with Eric Chen and Rugang Ye.
Ovidiu Munteanu (University of Connecticut, USA)
Ovidiu Munteanu (University of Connecticut, USA)
DATE: August 20, 2020, Thursday 2:00 PM.
DATE: August 20, 2020, Thursday 2:00 PM.
TITLE: Sobolev inequality and the topology at infinity of complete manifolds
TITLE: Sobolev inequality and the topology at infinity of complete manifolds
ABSTRACT: We study the number of ends of manifolds admitting a general Sobolev inequality and apply our results to obtain topological information for self-similar solutions of the Ricci flow and the Mean Curvature Flow. The method is based on a detailed analysis of positive solutions of a given Schrodinger equation on such manifolds.
ABSTRACT: We study the number of ends of manifolds admitting a general Sobolev inequality and apply our results to obtain topological information for self-similar solutions of the Ricci flow and the Mean Curvature Flow. The method is based on a detailed analysis of positive solutions of a given Schrodinger equation on such manifolds.
Giovanni Catino (Politecnico di Milano, Italy)
Giovanni Catino (Politecnico di Milano, Italy)
DATE: August 13, 2020, Thursday 2:00 PM.
DATE: August 13, 2020, Thursday 2:00 PM.
TITLE: Some canonical Riemannian metrics on four-dimensional manifolds: existence and rigidity
TITLE: Some canonical Riemannian metrics on four-dimensional manifolds: existence and rigidity
ABSTRACT: In this talk I will present some results concerning rigidity and existence of canonical metrics on closed four-dimensional Riemannian manifolds. In particular I will consider Einstein metrics, Harmonic Weyl metrics and some generalizations. These are joint works with P. Mastrolia (Università degli Studi di Milano), D.D. Monticelli and F. Punzo (Politecnico di Milano).
ABSTRACT: In this talk I will present some results concerning rigidity and existence of canonical metrics on closed four-dimensional Riemannian manifolds. In particular I will consider Einstein metrics, Harmonic Weyl metrics and some generalizations. These are joint works with P. Mastrolia (Università degli Studi di Milano), D.D. Monticelli and F. Punzo (Politecnico di Milano).
Guofang Wang (University of Freiburg, Germany)
Guofang Wang (University of Freiburg, Germany)
DATE: August 6, 2020, Thursday 2:00 PM.
DATE: August 6, 2020, Thursday 2:00 PM.
TITLE: The relative isoperimetric inequality for minimal submanifolds
TITLE: The relative isoperimetric inequality for minimal submanifolds
ABSTRACT: In this talk, we mainly consider the relative isoperimetric inequalities for minimal submanifolds with free boundary. We first generalize ideas of restricted normal cones given by Choe-Ghomi-Ritoré in 2006 and obtain an optimal area estimate for generalized restricted normal cones. This area estimate, together with the ABP method of Cabré, provides a new proof of the relative isoperimetric inequality obtained by Choe-Ghomi-Ritoré in 2007. Furthermore, with this estimate we use ideas of Brendle in his recent work in 2019 to prove an optimal relative isoperimetric inequality for minimal submanifolds with free boundary, which gives an affirmative answer to an open problem proposed by Choe in 2005, when the codimension is less than or equals to 2. (This is a joint work with Lei Liu and Liangjun Weng) .
ABSTRACT: In this talk, we mainly consider the relative isoperimetric inequalities for minimal submanifolds with free boundary. We first generalize ideas of restricted normal cones given by Choe-Ghomi-Ritoré in 2006 and obtain an optimal area estimate for generalized restricted normal cones. This area estimate, together with the ABP method of Cabré, provides a new proof of the relative isoperimetric inequality obtained by Choe-Ghomi-Ritoré in 2007. Furthermore, with this estimate we use ideas of Brendle in his recent work in 2019 to prove an optimal relative isoperimetric inequality for minimal submanifolds with free boundary, which gives an affirmative answer to an open problem proposed by Choe in 2005, when the codimension is less than or equals to 2. (This is a joint work with Lei Liu and Liangjun Weng) .
Page updated
Google Sites
Report abuse