Rectifiable Curves in Proximally Smooth Sets
Sign Up to like & getrecommendations! Published in 2021 at "Set-Valued and Variational Analysis"
DOI: 10.1007/s11228-021-00612-1
Abstract: We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve… read more here.
Keywords: rectifiable curves; smooth set; proximally smooth; curves proximally ... See more keywords
Subsets of rectifiable curves in Banach spaces II: Universal estimates for almost flat arcs
Sign Up to like & getrecommendations! Published in 2022 at "Illinois Journal of Mathematics"
DOI: 10.1215/00192082-10592390
Abstract: We prove that in any Banach space the set of windows in which a rectifiable curve resembles two or more straight line segments is quantitatively small with constants that are independent of the curve, the… read more here.
Keywords: banach spaces; spaces universal; curves banach; subsets rectifiable ... See more keywords