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Stochastic forms of functional isoperimetric inequalities
(University of Missouri--Columbia, 2021)
The Brunn-Minkowski and Prekopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions, so it seems that ...
Structural features of persistent homology and their algorithmic transformations
(University of Missouri--Columbia, 2021)
We re-examine the theory and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common ...
The poisson problem on Lipschitz domains
(University of Missouri--Columbia, 2005)
domains. The main theorems we prove extend the work of D. Jerison and C. Kenig [JFA, 95], whose methods and results are largely restricted to the case p_ 1, and answer the open problem #3.2.21 on p. 121 in C. Kenig's book in the most complete fashion. When...