Manifolds of mappings for continuum mechanics

Abstract

This is an overview article. After an introduction to convenient calculus in infinite dimensions, the foundational material for manifolds of mappings is presented. The central character is the smooth convenient manifold $C^{\infty }(M,N)$ of all smooth mappings from a finite dimensional Whitney manifold germ $M$ into a smooth manifold $N$. A Whitney manifold germ is a smooth (in the interior) manifold with a very general boundary, but still admitting a continuous Whitney extension operator. This notion is developed here for the needs of geometric continuum mechanics.

66 pages. arXiv admin note: substantial text overlap with arXiv:1505.02359, arXiv:math/9202208. Last version: some misprintscorrected

References in corpus (1)

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

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