A Study on Some Spectral Invariants on Cauchy-Riemann Manifolds with Group Action(2/2)

Project Details

Description

In this project the PI plan to study the asymptotic expansion of the analytic torsion on a compact CR manifold of high codimension with a compact Lie group locally free CR action. Recently S. Finski generalized the Bismut-Vasserot asymptotic formula to setting of compact complex orbifolds. This project should be closely related to the results of Finski on Bismut-Vasserot's asymptotic formula on compact complex orbifolds. One other possible application will be a generalization of the Bismut-Vasserot asymptotic formula for symmetric powers of a positive vector bundle over a compact complex manifold.Another project is jointly with Chin-Yu Hsiao (Academia Sinica) and Guokuan Shao (Sun Yat-Sen University (Zhuhai), China), we study G-equivariant Szego kernels on a compact CR manifold with compact Lie group action G associated with all equivalent classes of irreducible unitary representations of G. We shall establish G-equivariant Boutet de Monvel-Sjostrand type theorems. When the CR manifold is strongly pseudoconvex with S^1 action, we shall compute coefficients of the first few terms of the asymptotic expansions of G-equivariant Szego kernel functions. The main tool of our appraoch is Hormander's stationary phase formula. We expect that the coefficients of the first few lower order terms of the G-equivalent Szego kernel function's expansion for functions will contain some geometric quantities.
StatusActive
Effective start/end date1/08/2131/07/22

UN Sustainable Development Goals

In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):

  • SDG 16 - Peace, Justice and Strong Institutions
  • SDG 17 - Partnerships for the Goals

Keywords

  • Szego kernel
  • analytic torsion
  • CR manifold

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