Green's functions on minimal submanifolds.
Green's functions on minimal submanifolds.
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Yifan Guo, University of California Irvine
Fine Hall 314
In this talk, we are going to discuss the following properties of Green's function on a minimal submanifold with singularity in R^n: lower and upper bounds, asymptotics near the pole and infinity as well as 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 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.