On the Whitney extension problem for near isometries and beyond

• URL: http://arxiv.org/abs/2103.09748v1
• Date: Wed, 17 Mar 2021 16:12:53 GMT
• Title: On the Whitney extension problem for near isometries and beyond
• Authors: Steven B. Damelin
• Abstract summary: A significant portion of the work is based on joint research with Charles Fefferman. The topics of this work include (a) The space of maps of bounded mean oscillation (BMO) in $mathbb RD,, Dgeq 2$. The labeled and unlabeled near alignment and Procrustes problem for point sets with certain geometries and for not too thin compact sets both in $mathbb RD,, Dgeq 2$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper is an exposition of work of the author et al. detailing fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic-differential geometry, analysis on manifolds, complex-harmonic analysis, data science, partial differential equations, optimization and probability. A significant portion of the work is based on joint research with Charles Fefferman in the papers [39, 40, 41, 42]. The topics of this work include (a) The space of maps of bounded mean oscillation (BMO) in $\mathbb R^D,\, D\geq 2$. (b) The labeled and unlabeled near alignment and Procrustes problem for point sets with certain geometries and for not too thin compact sets both in $\mathbb R^D,\, D\geq 2$. (c) The Whitney near isometry extension problem for point sets with certain geometries and for not too thin compact sets both in $\mathbb R^D,\, D\geq 2$. (d) Partitions and clustering of compact sets and point sets with certain geometries in $\mathbb R^D,\, D\geq 2$ and analysis on certain manifolds in $\mathbb R^D,\, D\geq 2$. Many open problems for future research are given.

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