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Rough metrics on ma...
Rough metrics on manifolds and quadratic estimates
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- Bandara, Lashi, 1981 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics
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- Bandara, Menaka Lashitha, 1981 (författare)
- Chalmers tekniska högskola,Chalmers University of Technology,Göteborgs universitet,University of Gothenburg
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(creator_code:org_t)
- 2016-03-05
- 2016
- Engelska.
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 283:3, s. 1245-1281
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Rough metrics
- Quadratic estimates
- Kato square root problem
- Quadratic estimates
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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