Rigidity of holomorphic map between bounded symmetric domains preserving Shilov boundaries

Speaker: Yun GAO (Shanghai Jiao Tong University)

Time: 15th May, 10:00 ~ 12:00, Thursday

Location: R1310, SIMIS
Zoom Meeting ID: 838 524 0106 (Passcode: SIMIS)

Abstract:The study of rigidity of holomorphic maps originated from the work of Poincaré and later Alexander for maps sending one open piece of the sphere into another. Webster obtained rigidity for holomorphic maps between pieces of spheres of different dimension, proving that any such map between spheres in C^n and C^{n+1} is totally geodesic. There are plenty of results about the holomorphic proper mapping between balls and generalized balls. The rigidity for maps between bounded symmetric domains are more complicated. Mok conjectures that If the rank r of D does not exceed the rank r’ of D’ and both ranks r,r’ >1, then the proper holomorphic maps is totally geodesic. There are some results about this conjecture. In 2007, Kim and Zaitsev proved the rigidity of locally defined CR embeddings between Shilov boundaries of general Cartan type I bounded symmetric domains of higher rank. In this talk, we will introduce a different method coming from algebraic geometry to study this kind of map and prove the rigidity of holomorphic mapping between bounded symmetric domains preserving Shilov boundaries from rank 1 to higher rank.