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Rough metrics on manifolds and quadratic estimates

Lashi Bandara (Institutionen för matematiska vetenskaper, matematik)
Mathematische Zeitschrift (0025-5874). Vol. 283 (2016), 3, p. 1245–1281.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Rough metrics, Quadratic estimates, Kato square root problem



Denna post skapades 2016-04-01. Senast ändrad 2016-08-26.
CPL Pubid: 233976

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys
Geometri

Chalmers infrastruktur