Rough metrics on manifolds and quadratic estimates
Journal article, 2016

We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of “rough” Riemannian-like metrics that are permitted to be of low regularity and degenerate on sets of measure zero. We also demonstrate how to transmit quadratic estimates between manifolds which are homeomorphic and locally bi-Lipschitz. As a consequence, we demonstrate the invariance of the Kato square root problem under Lipschitz transformations and obtain solutions to this problem on functions and forms on compact manifolds with a rough metric. Furthermore, we show that a lower bound on the injectivity radius is not a necessary condition to solve the Kato square root problem.

Quadratic estimates

Rough metrics

Kato square root problem

Author

Menaka Lashitha Bandara

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 283 3 1245-1281

Subject Categories

Geometry

Mathematical Analysis

DOI

10.1007/s00209-016-1641-x

More information

Created

10/8/2017