Manifolds of Mappings for Continuum Mechanics (Q3300563)

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English	Manifolds of Mappings for Continuum Mechanics	scientific article

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scholarly article

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Manifolds of Mappings for Continuum Mechanics (English)

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Peter W. Michor

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Advances in Mechanics and Mathematics

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publication date

29 July 2020

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full work available at URL

https://arxiv.org/abs/1909.00445

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zbMATH Keywords

diffeomorphism group

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shape space

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weak Riemannian metric

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regular Lie group

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Differentiable mappings on products with different degrees of differentiability in the two factors

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Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits

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Spaces of Whitney Functions on Cantor-Type Sets

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Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

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Soliton solutions for the elastic metric on spaces of curves

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Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

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Homogeneous Sobolev metric of order one on diffeomorphism groups on real line

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Overview of the geometries of shape spaces and diffeomorphism groups

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Local and global well-posedness of the fractional order EPDiff equation on \(\mathbb{R}^d\)

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Sobolev metrics on shape space of surfaces

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Almost Local Metrics on Shape Space of Hypersurfaces in<i>n</i>-Space

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Sobolev metrics on the manifold of all Riemannian metrics

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Extension of Whitney fields from subanalytic sets

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Differentiability of a Function and of its Compositions with Functions of One Variable.

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TEN TOPOLOGIES FOR <i>X</i> × <i>Y</i>

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FUNCTION SPACES AND PRODUCT TOPOLOGIES

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Completeness properties of Sobolev metrics on the space of curves

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GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES

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On completeness of groups of diffeomorphisms

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The action of the diffeomorphism group on the space of immersions

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Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)

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Groups of diffeomorphisms and the motion of an incompressible fluid

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Geometry of manifolds of maps

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Geodesic completeness for Sobolev \(H^{s}\)-metrics on the diffeomorphism group of the circle

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Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle

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Überblick über die Theorie der analytischen Funktionale und ihre Anwendungen

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\(C^m\) extension by linear operators

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Extension operators for spaces of infinite differentiable Whitney jets

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Tame linear extension operators for smooth Whitney functions

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Whitney extension operators without loss of derivatives

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Principal bundles of embeddings and nonlinear Grassmannians

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Complete metrics of bounded curvature on noncompact manifolds

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Kinematical uniqueness of homogeneous isotropic LQC

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Closed surfaces with different shapes that are indistinguishable by the SRNF

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\(L^ p\)-theory of elliptic differential operators on manifolds of bounded geometry

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The convenient setting for real analytic mappings

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The convenient setting for non-quasianalytic Denjoy-Carleman differentiable mappings

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The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings

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The convenient setting for Denjoy-Carleman differentiable mappings of Beurling and Roumieu type

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An exotic zoo of diffeomorphism groups on \(\mathbb {R}^n\)

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The exponential law for spaces of test functions and diffeomorphism groups

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On a differential structure for the group of diffeomorphisms

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Half-Lie groups

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Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks

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Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

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Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms

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Riemannian geometries on spaces of plane curves

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An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach

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A zoo of diffeomorphism groups on \(\mathbb R^n\)

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APPROXIMATE DIMENSION AND BASES IN NUCLEAR SPACES

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On Euler's equation and `EPDiff'

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On time-dependent Besov vector fields and the regularity of their flows

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On groups of Hölder diffeomorphisms and their regularity

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The Trouvé group for spaces of test functions

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On regular Frechet-Lie groups. I: Some differential geometrical expressions of Fourier-integral operators on a Riemannian manifold

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On regular Frechet-Lie groups. II: Composition rules of Fourier-integral operators on a Riemannian manifold

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On regular Frechet-Lie groups. III: A second cohomology class related to the Lie algebra of pseudo-differential operators of order one

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On regular Frechet-Lie groups. IV: Definition and fundamental theorems

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On regular Frechet-Lie groups. V: Several basic properties

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On regular Fréchet-Lie groups. VI: Infinite dimensional Lie groups which appear in general relativity

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Extension of C ∞ Functions Defined in a Half Space

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A convenient category of topological spaces

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Natural bundles. III. Resolving the singularities in the space of immersed submanifolds

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Fortsetzungen von \(C^\infty\)-Funktionen, welche auf einer abgeschlossenen Menge in \(R^ n\) definiert sind

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A geometric characterization for the property \((DN)\) of \(\mathcal{E}(K)\) for arbitrary compact subsets \(K\) of \(\mathbb{R}\)

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Stokes' formula for stratified forms

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Identifiers

zbMATH Open document ID

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10.1007/978-3-030-42683-5_1

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3300563

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