# 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

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topFu, 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 -

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