Search results for "Finsler manifold"

showing 4 items of 4 documents

Wulff shape characterizations in overdetermined anisotropic elliptic problems

2017

We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.

Applied Mathematics010102 general mathematicsDegenerate energy levelsMathematical analysisMathematics::Analysis of PDEsElliptic pdesComputer Science::Numerical Analysis01 natural sciencesMathematics::Numerical Analysis010101 applied mathematicsOverdetermined systemMathematics - Analysis of PDEsNonlinear Sciences::Exactly Solvable and Integrable SystemsSettore MAT/05 - Analisi MatematicaOverdetermined problems. Finsler manifold. Wulff shapes. Torsion problem. CapacityFOS: MathematicsMathematics::Differential GeometryFinsler manifold0101 mathematicsAnisotropyAnalysisAnalysis of PDEs (math.AP)Mathematics
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Infinitesimal Hilbertianity of Weighted Riemannian Manifolds

2018

AbstractThe main result of this paper is the following: anyweightedRiemannian manifold$(M,g,\unicode[STIX]{x1D707})$,i.e., a Riemannian manifold$(M,g)$endowed with a generic non-negative Radon measure$\unicode[STIX]{x1D707}$, isinfinitesimally Hilbertian, which means that its associated Sobolev space$W^{1,2}(M,g,\unicode[STIX]{x1D707})$is a Hilbert space.We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold$(M,F,\unicode[STIX]{x1D707})$can be isometrically embedded into the space of all measurable sections of the tangent bundle of$M$that are$2$-integrable with respect to$\unicode[STIX]{x1D707}$.By following the…

Mathematics - Differential GeometryMathematics::Functional AnalysisPure mathematicsGeneral MathematicsInfinitesimal010102 general mathematicsRiemannian manifold01 natural sciencesSobolev spacedifferentiaaligeometriasymbols.namesakeDifferential Geometry (math.DG)0103 physical sciencesFOS: MathematicssymbolsMathematics::Metric Geometry53C23 46E35 58B20010307 mathematical physicsFinsler manifoldMathematics::Differential Geometry0101 mathematicsmonistotCarnot cyclefunktionaalianalyysiMathematics
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Universal infinitesimal Hilbertianity of sub-Riemannian manifolds

2019

We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.

Mathematics - Differential GeometryMetric Geometry (math.MG)Sobolev spaceFunctional Analysis (math.FA)Mathematics - Functional AnalysisRiemannin monistotdifferentiaaligeometriasub-Finsler manifoldMathematics - Metric GeometryDifferential Geometry (math.DG)infinitesimal hilbertianityFOS: MathematicsMathematics::Metric Geometrysub-Riemannian manifoldMathematics::Differential GeometrymonistotfunktionaalianalyysiMathematics::Symplectic Geometry53C23 46E35 53C17 55R25Analysis
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A short survey on Lie theory and Finsler geometry

2017

The aim of this chapter is to provide readers with a common thread to the many topics dealt with in this book, which is intermediate and which aims at postgraduate students and young researchers, wishing to intrigue those who are not experts in some of the topics. We also hope that this book will contribute in encouraging new collaborations among disciplines which have stemmed from related problems. In this context, we take the opportunity to recommend the book by Hawkins [18]. A basic bibliography is outlined between the lines.

Settore MAT/05 - Analisi MatematicaBibliographyFinsler manifoldThread (computing)Lie theorySettore MAT/03 - GeometriaTopologyGeneralLiterature_REFERENCE(e.g.dictionariesencyclopediasglossaries)MathematicsEpistemologyLie groups and Lie algebras non associative algebra Finsler Geometry
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