Manifolds of continuous BV-functions and vector measure regularity of Banach–Lie groups
Helge Glöckner, Alexander Schmeding, Ali Suri · Geometric Mechanics · 2024
We construct a smooth Banach-manifold [Formula: see text] whose elements are suitably defined functions [Formula: see text] of bounded variation with values in a smooth Banach manifold [Formula: see text] which admits a local addition. If the target manifold is a Banach–Lie group [Formula: see text], with Lie algebra [Formula: see text], we obtain an infinite-dimensional Banach–Lie group [Formula: see text] with Lie algebra [Formula: see text]. Strengthening known regularity properties of Banach–Lie groups, we construct a smooth evolution map from a Banach space of [Formula: see text]-valued vector measures on [Formula: see text] to [Formula: see text].