Sponsored by
 
Events
News
 
[ Events ]
 
 

Activity Search
Sort out
Field
 
Year
Seminars  
 
NCTS Differential Geometry Seminar
 
16:00 - 17:00, April 26, 2018 (Thursday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Biholomorphically Invariant Curves and Surfaces on the Boundary of a Strongly Pseudoconvex Domain in C^2
Jih-Hsin Cheng (Academia Sinica)

Abstract:

I will talk about biholomorphically invariant curves and surfaces on the boundary of a strongly pseudoconvex domain in . A distinguished class of such invariant curves satisfies a system of 2nd order ODEs, called chains in CR geometry. We interpret chains as geodesics of a Kropina metric in Finsler geometry. The associated energy functional of a curve on the boundary can be recovered as the log term coefficient in a weighted renormalized area expansion of a minimal surface that it bounds inside the domain. For surfaces, we express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler-Lagrange equations of the associated energy functionals. Many solutions are given and discussed. In relation to the singular CR Yamabe problem, we show that one of the energy functionals appears as the coefficient (up to a constant multiple) of the log term in the associated volume renormalization.



 

back to list  
 (C) 2021 National Center for Theoretical Sciences