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of 273
pro vyhledávání: '"Michor, Peter W."'
We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1-form of the Marsden-Weinstein structure with Riemannian structures th
Externí odkaz:
http://arxiv.org/abs/2407.19908
Autor:
Michor, Johanna, Michor, Peter W.
The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold $M$ to a smooth mapping from $M$ into the Lie group. In this paper this is generalized to infinite dimensional $M$ for infin
Externí odkaz:
http://arxiv.org/abs/2404.05416
Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely required to be continuous. The main examples are groups of $H^s$ or $C^k$ di
Externí odkaz:
http://arxiv.org/abs/2302.01631
Autor:
Kamber, Franz W., Michor, Peter W.
In [4] and [5], we generalized the concept of completion of an infinitesimal group action $\zeta : {\mathfrak g} \to \mathfrak X (M)$ to an actual group action on a (non-compact) manifold $M$, originally introduced by R. Palais [9], and showed by exa
Externí odkaz:
http://arxiv.org/abs/2209.15432
Publikováno v:
Differential Geometry and its Applications Volume 90, October 2023, 102029
In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an $n$-sample in a space $M$ can be considered as an e
Externí odkaz:
http://arxiv.org/abs/2010.08039
Publikováno v:
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XXIV (2023), 1895-1948
We study completeness properties of reparametrization invariant Sobolev metrics of order $n\ge 2$ on the space of manifold valued open and closed immersed curves. In particular, for several important cases of metrics, we show that Sobolev immersions
Externí odkaz:
http://arxiv.org/abs/2007.13315
Publikováno v:
In Differential Geometry and its Applications October 2023 90
Autor:
Klassen, Eric, Michor, Peter W.
Publikováno v:
Achivum Mathematicum (Brno) 56 (2020), 107-114
The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [3], provides a way of representing immersed surfaces in $\mathbb R^3$, and equipping the set of these immersions with a "distance function" (to be precise, a pseudometric) that is e
Externí odkaz:
http://arxiv.org/abs/1910.10804
Publikováno v:
Calculus of Variations and Partial Differential Equations 59, 62 (2020)
We prove that the geodesic equations of all Sobolev metrics of fractional order one and higher on spaces of diffeomorphisms and, more generally, immersions are locally well posed. This result builds on the recently established real analytic dependenc
Externí odkaz:
http://arxiv.org/abs/1909.08657