Calculus, fractals, and analysis on metric spaces
Stephen Semmes
TL;DR
This paper explores the mathematical properties of fractal sets and develops analytical tools for studying functions defined on these complex metric spaces, advancing understanding in fractal analysis.
Contribution
It introduces new methods for analysis on fractal metric spaces, bridging calculus and fractal geometry in a novel way.
Findings
Characterization of fractal sets in metric spaces
Development of analytical techniques for fractal functions
Insights into the structure of fractal measures
Abstract
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · advanced mathematical theories