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  • Bandara, Lashi, 1981, et al. (author)
  • Rough metrics on manifolds and quadratic estimates
  • 2016
  • In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 283:3, s. 1245-1281
  • Journal article (peer-reviewed)abstract
    • 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.
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Type of publication
journal article (1)
Type of content
peer-reviewed (1)
Author/Editor
Bandara, Lashi, 1981 (1)
Bandara, Menaka Lash ... (1)
University
University of Gothenburg (1)
Chalmers University of Technology (1)
Language
English (1)
Research subject (UKÄ/SCB)
Natural sciences (1)
Year
2016 (1)

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