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Schauder estimates on products of cones
journal contributionposted on 2023-11-09, 14:43 authored by Martin de BorbonMartin de Borbon, Gregory Edwards
We prove an interior Schauder estimate for the Laplacian on metric products of two dimensional cones with a Euclidean factor, generalizing the work of Donaldson and reproving the Schauder estimate of Guo–Song. We characterize the space of homogeneous subquadratic harmonic functions on products of cones, and identify scales at which geodesic balls can be well approximated by balls centered at the apex of an appropriate model cone. We then locally approximate solutions by subquadratic harmonic functions at these scales to measure the Hölder continuity of second derivatives.
Curvature constraints and space of metrics – CCEM
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National Science Foundation RTG: Geometry and Topology at the University of Notre Dame, grant number DMS1547292
- Mathematical Sciences
Published inCommentarii Mathematici Helvetici
Pages113 - 148
- AM (Accepted Manuscript)
Rights holder© EMS Press
Publisher statementThis paper was accepted for publication in the journal Commentarii Mathematici Helvetici and the definitive published version is available at https://doi.org/10.4171/CMH/509