Home /  Graduate Student Seminar Series: The pressure metric on quasi-Fuchsian space & Green's functions on minimal submanifolds

Seminar

Graduate Student Seminar Series: The pressure metric on quasi-Fuchsian space & Green's functions on minimal submanifolds October 15, 2024 (11:00 AM PDT - 12:30 PM PDT)
Parent Program:
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Yifan Guo (University of California, Irvine), Frieder Jaeckel (Universität Bonn)
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Keywords and Mathematics Subject Classification (MSC)
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Video

Green's functions on minimal submanifolds

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Frieder Jäckel: The pressure metric on quasi-Fuchsian space

Abstract: Quasi-Fuchsian space is a moduli space of certain hyperbolic 3-manifolds and it can be equipped with a metric, called the pressure metric, whose definition is inspired by the definition of the Weil-Petersson metric on Teichmüller space. We will discuss that the pressure metric on quasi-Fuchsian space has finite diameter, why this is interesting, and how it relates to the study of eigenfunctions. The talk is based on joint work with E. Fioravanti, U. Hamenstädt and Y. Zhang

 

Yifan Guo: Green's functions on minimal submanifolds

Abstract: We are going to discuss the following properties of Green's function on a minimal submanifold with singularities : lower and upper bounds, asymptotics near the pole and infinity as well as $C^{\alpha}$ convergence under convergence of minimal submanifolds. We show that the Green's functions on area-minimizing boundaries have all of the mentioned properties. We also have $L^p$ convergence of the Green's functions for converging multiplicity 1 stationary varifolds. Outside of these classes of minimal submanifolds, the properties may fail and we discuss the reasons and some examples.

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Green's functions on minimal submanifolds