Piecewise linear approximation of smooth functions of two variables

Joseph H.G. Fu[1]

  • [1] Department of Mathematics University of Georgia Athens GA 30602 USA

Actes des rencontres du CIRM (2013)

  • Volume: 3, Issue: 1, page 11-16
  • ISSN: 2105-0597

Abstract

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The normal cycle of a singular subset X of a smooth manifold is a basic tool for understanding and computing the curvature of X . If X is replaced by a singular function on n then there is a natural companion notion called the gradient cycle of f , which has been introduced by the author and by R. Jerrard. We discuss a few fundamental facts and open problems about functions f that admit gradient cycles, with particular attention to the first nontrivial dimension n = 2 .

How to cite

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Fu, Joseph H.G.. "Piecewise linear approximation of smooth functions of two variables." Actes des rencontres du CIRM 3.1 (2013): 11-16. <http://eudml.org/doc/275298>.

@article{Fu2013,
abstract = {The normal cycle of a singular subset $X$ of a smooth manifold is a basic tool for understanding and computing the curvature of $X$. If $X$ is replaced by a singular function on $\{\mathbb\{R\}\}^n$ then there is a natural companion notion called the gradient cycle of $f$, which has been introduced by the author and by R. Jerrard. We discuss a few fundamental facts and open problems about functions $f$ that admit gradient cycles, with particular attention to the first nontrivial dimension $n=2$.},
affiliation = {Department of Mathematics University of Georgia Athens GA 30602 USA},
author = {Fu, Joseph H.G.},
journal = {Actes des rencontres du CIRM},
keywords = {graph theory; shape recognition; optimal transportation},
language = {eng},
month = {11},
number = {1},
pages = {11-16},
publisher = {CIRM},
title = {Piecewise linear approximation of smooth functions of two variables},
url = {http://eudml.org/doc/275298},
volume = {3},
year = {2013},
}

TY - JOUR
AU - Fu, Joseph H.G.
TI - Piecewise linear approximation of smooth functions of two variables
JO - Actes des rencontres du CIRM
DA - 2013/11//
PB - CIRM
VL - 3
IS - 1
SP - 11
EP - 16
AB - The normal cycle of a singular subset $X$ of a smooth manifold is a basic tool for understanding and computing the curvature of $X$. If $X$ is replaced by a singular function on ${\mathbb{R}}^n$ then there is a natural companion notion called the gradient cycle of $f$, which has been introduced by the author and by R. Jerrard. We discuss a few fundamental facts and open problems about functions $f$ that admit gradient cycles, with particular attention to the first nontrivial dimension $n=2$.
LA - eng
KW - graph theory; shape recognition; optimal transportation
UR - http://eudml.org/doc/275298
ER -

References

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