Some aspects of calculus on non-smooth sets
Stephen Semmes
TL;DR
This paper explores properties of non-smooth sets in R^n that allow for controlled-length connecting paths, advancing understanding of their geometric and analytic structure.
Contribution
It introduces a framework for analyzing sets in R^n with path-connectedness properties related to their metric structure.
Findings
Characterization of sets with bounded-length connecting paths
Insights into the geometric structure of non-smooth sets
Potential applications in analysis on irregular sets
Abstract
Sets in R^n in which every pair of elements x, y can be connected by a path in the set of length bounded by a constant multiple of the distance between x and y are considered.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Advanced Banach Space Theory