arXiv subjects

Jacob Honeycutt

Publications and source records attributed to Jacob Honeycutt.

3 recordsLinked to original sources

arXiv2025

Quasisymmetric rectifiability of uniformly disconnected sets

We prove that uniformly disconnected subsets of metric measure spaces with controlled geometry (complete, Ahlfors regular, supporting a Poincare inequality, and a mild topological condition) are contained in a quasisymmetric arc. This generalizes a result of MacManus in 1999 from Euclidean spaces to abstract metric setting. Along the way, we prove a geometric strengthening of the classical Denjoy-Riesz theorem in metric measure spaces. Finally, we prove that the complement of a uniformly disconnected set in such a metric space is uniform, quantitatively.

math.MG↗

arXiv2024

Bi-Lipschitz arcs in metric spaces with controlled geometry

We generalize a bi-Lipschitz extension result of David and Semmes from Euclidean spaces to complete metric measure spaces with controlled geometry (Ahlfors regularity and supporting a Poincaré inequality). In particular, we find sharp conditions on metric measure spaces $X$ so that any bi-Lipschitz embedding of a subset of the real line into $X$ extends to a bi-Lipschitz embedding of the whole line. Along the way, we prove that if the complement of an open subset $Y$ of $X$ has small Assouad dimension, then it is a uniform domain. Finally, we prove a quantitative approximation of continua in $X$ by bi-Lipschitz curves.

math.MG↗

arXiv2021

Closed Neighborhood Ideals of Finite Simple Graphs

We investigate Sharifan and Moradi's closed neighborhood ideal of a finite simple graph, which is a square-free monomial ideal in a polynomial ring over a field. We explicitly describe the minimal irreducible decompositions of these ideals. We also characterize the trees whose closed neighborhood ideals are Cohen-Macaulay; in particular, this property for closed neighborhood ideals of trees is characteristic independent.

math.AC↗