Rigidity Theorems by Capacities and Kernels
نویسندگان
چکیده
Abstract For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, logarithmic capacity $c_{\beta }$, and analytic $c_{B}$ satisfy inequality chain $\pi K \geq c^2_{\beta } c^2_B$. Moreover, equality holds at a single point between two of three quantities if only $X$ is biholomorphic to disk possibly less relatively closed polar set. We extend by showing that $c_{B}^2 \pi v^{-1}(X)$ on planar domains, where $v(\cdot )$ Euclidean volume, characterize extremal cases when one point. Similar rigidity theorems concerning Szegö kernel, higher-order kernels, sublevel sets Green’s function are also developed. Additionally, we explore phenomena related multi-dimensional Suita conjecture.
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2022
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnac290