Zobrazeno 1 - 10
of 326
pro vyhledávání: '"Zimmerman Scott"'
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 11, Iss 1, Pp 35-55 (2023)
We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R. Schul in Euclidean space, for an
Externí odkaz:
https://doaj.org/article/cbf50c31be274108ac551616e6474aab
Autor:
Zimmerman, Scott
This paper gives an alternate, elementary proof of a result of Magnani: maps between Carnot groups that preserve horizontal curves and are continuously differential in horizontal directions in the Euclidean sense are continuously Pansu differentiable
Externí odkaz:
http://arxiv.org/abs/2405.12138
Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group
In the setting of horizontal curves in the Heisenberg group, we prove a $C^{m,\omega}$ finiteness principle, a $C^{m,\omega}$ Lusin approximation result, a $C^{\infty}$ Whitney extension result, and a $C^{\infty}$ Lusin approximation result. Combined
Externí odkaz:
http://arxiv.org/abs/2310.06953
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 Poincar\'e inequality). In particular, we find sharp conditions on
Externí odkaz:
http://arxiv.org/abs/2307.06931
Autor:
Hajłasz Piotr, Zimmerman Scott
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 3, Iss 1 (2015)
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away f
Externí odkaz:
https://doaj.org/article/429bff788afa4eb484947433418283c4
Autor:
Orban, Chris, Zimmerman, Scott, Kulp, Jessica T., Boughton, Jennifer, Perrico, Zach, Rapp, Brianna, Teeling-Smith, Richelle
Recent years have seen an explosion of interest in analyzing the motion of objects in video data as a way for students to connect the concepts of physics to something tangible like a video recording of an experiment. A variety of software exists for
Externí odkaz:
http://arxiv.org/abs/2206.07909
Autor:
Speight, Gareth, Zimmerman, Scott
We characterize which mappings from a compact subset of $\mathbb{R}$ into the Heisenberg group can be extended to a $C^{m,\omega}$ horizontal curve for a given modulus of continuity $\omega$. We motivate our characterization by showing that the $C^{m
Externí odkaz:
http://arxiv.org/abs/2204.03544
We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of the first author and R. Schul in Euclidean space,
Externí odkaz:
http://arxiv.org/abs/2109.06753
Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group
Publikováno v:
In Journal de mathématiques pures et appliquées August 2024 188:320-344