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Geometric Analysis Seminar

Canonical identification between scales on Ricci-flat manifolds

Jiewon Park, MIT,

Location:  Hill 705
Date & time: Tuesday, 11 February 2020 at 2:50PM - 3:50PM

Abstract: We will discuss geometric applications of the Laplace equation on a complete Ricci-flat manifold with Euclidean volume growth. We will focus on how to identify two arbitrarily far apart scales in the manifold in a natural way, exploiting the ?ojasiewicz inequality of Colding-Minicozzi, in the case when a tangent cone at infinity has smooth cross section. We also prove a matrix Harnack inequality for the Green function when there is an additional condition on sectional curvature, which is an analogue of various matrix Harnack inequalities obtained by Hamilton and Li-Cao in different time-dependent settings.


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