7 papers
Group Contractions via Infinite-Dimensional Lie Theory
David Prinz, Alexander Schmeding, Philip K. Schwartz
Contractions are a procedure to construct a new Lie algebra out of a given one via a singular limit. Specifically, the Ä°nönü--Wigner construction starts with a Lie algebra $\mat…
Optimization on Weak Riemannian Manifolds
Valentina Zalbertus, Max Pfeffer, Alexander Schmeding
Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds whic…
Cotangent Bundles as Coadjoint Orbits and Asymptotic Character Formulas
Michael Gjertsen, Alexander Schmeding
The present article presents geometric quantization on cotangent bundles as a special instance of Kirillov's orbit method. To this end, the cotangent bundle is realized as a coadjo…
The Stacey-Roberts Lemma for Banach Manifolds
Peter Kristel, Alexander Schmeding
The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by…
On the singularities of the exponential function of a semidirect product
Alexandru Chirvasitu, Rafael Dahmen, Karl-Hermann Neeb +1
We show that the Fréchet--Lie groups of the form resulting from smooth flows on compact manifolds fail to be locally exponential in several c…
Boundary values of diffeomorphisms of simple polytopes, and controllability
Helge Glöckner, Erlend Grong, Alexander Schmeding
We consider the Lie group of smooth diffeomorphisms Diff of a simple polytope in the euclidean space. Simple polytopes are special cases of manifolds with corners. The geo…