Informal Geometric Analysis Seminar

Fall 2019

Organizers: V. Tosatti, B. Weinkove, S. Zelditch

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The seminar met on Thursdays from 3.00pm to 4.00pm in Lunt 107.

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Schedule

• October 3
  Man-Chun Lee - Gromov Hausdorff limit of complete Kähler manifolds with BK lower bound via partial Kähler Ricci flow

• October 10
  Sisi Shen - Estimates for constant Chern scalar curvature - Reference

• October 17
  Heming Jiao (Harbin Institute of Technology) - The Dirichlet problem for Hessian type equations

• November 7
  Nick McCleerey - Superforms, supercurrents, minimal manifolds and Riemannian geometry - Reference

• November 14
  Da Rong Cheng (University of Chicago) - Bubble tree convergence of conformally cross product preserving maps - Reference

• November 21
  Xiaoxiao Li (Notre Dame) - Asymptotic expansions of singular solutions of σ_k-Yamabe equation near isolated singularities - Abstract

  The classical Yamabe problem asks whether there is a metric with constant scalar curvature in a given conformal class. In general, we can ask the same question for the σ_k curvature, which is defined as the k^th elementary symmetric polynomial of the eigenvalues of the Schouten tensor. This is known as the σ_k-Yamabe problem. We consider the solutions to these questions with non-removable isolated singularities, that is the resulting conformal factor goes to infinity on a discrete set. Geometrically, it means the metric is complete on the complement or has some singularities. The main question is to understand the asymptotic behavior of such singular solutions near the singularities. We present a complete characterization when 1≤k<n (dimension of the manifold) by determining the asymptotic expansions for such solutions up to any order.

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Schedule for the past years:

2012-13 - 2013-14 - 2014-15 - 2015-16 - 2016-17 - 2017-18 - 2018-19