arXiv subjects

Matthias Kemper

Publications and source records attributed to Matthias Kemper.

2 recordsLinked to original sources

arXiv2022

Potential Theory on Gromov Hyperbolic Spaces

Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Here we extend Ancona's potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov hyperbolic metric measure spaces, unifying these settings in a common framework ready for applications to singular spaces such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack inequalities and a complete classification of positive harmonic functions in terms of the Martin boundary which is identified with the geometric Gromov boundary.

math.DG↗

arXiv2018

Potential Theory on Gromov Hyperbolic Manifolds of Bounded Geometry

In the 1980s Alano Ancona developed a profound potential theory on Gromov hyperbolic manifolds of bounded geometry. Since then, such hyperbolic spaces have become basic in geometry, topology and group theory. In this paper we make Ancona's original work, addressed to a rather advanced audience, approachable for a wider readership without firm background in potential theory. We streamline the arguments to make the results depend only on coarse geometro-analytic invariants and we derive useful details not found in the original sources. We explain remarkable relations of these results to recent developments in the potential theory and quasi-conformal geometry of Euclidean domains.

math.DG↗