# Seminars & Colloquia Calendar

Complex Analysis and Geometry Seminar

## "Rigidity theorems for invariant harmonic functions on bounded symmetric domains"

#### Song-Ying Li , UC Irvine

Location:  HILL 705
Date & time: Friday, 21 April 2017 at 10:30AM -

 Time: 10:30 AM Location: Hill 705 Abstract: Let $$Delta_g$$ be the Laplace-Beltrami operator in Bergman metric in the unit ball in $$C^n$$. Then the boundary value problem: $Delta_g u=0, hbox{ in } B_n; quad u=phi hbox{ on }d B_n$has a unique solution $u(z)=P[phi]=int_{d B_n} {(1-|z|^2)^n over |1-langle z, wrangle|^{2n}} phi(w) dsigma(w)$It well known that even if $$phiin C^infty(d B_n)$$, $$P[phi]$$ may not be in $$C^n(overline{B_n})$$. A well known theorem of R. Graham says that if $$u$$ is invariant harmonic in $$B_n$$ and $$C^n(overline{B_n})$$, then $$u$$ must be pluriharmonic in $$B_n$$. In this talk, I will present a joint work with R-Y. Chen, we try to generalize Graham's theorem to the bounded symmetric domains.

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