Seminars & Colloquia Calendar
"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 -
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| 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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