Extension of the unit normal vector field from a hypersurface

Roland Duduchava; Eugene Shargorodsky; George Tephnadze

doi:10.1515/gmj-2015-0036

Extension of the unit normal vector field from a hypersurface

Roland Duduchava^*, Eugene Shargorodsky, George Tephnadze

^*Corresponding author for this work

Tbilisi State University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.

Original language	English
Pages (from-to)	355-359
Number of pages	5
Journal	Georgian Mathematical Journal
Volume	22
Issue number	3
Early online date	31 Jul 2015
DOIs	https://doi.org/10.1515/gmj-2015-0036
Publication status	Published - Sept 2015

Keywords

extended normal vector field
Hypersurface
proper extension
unit normal vector field

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10.1515/gmj-2015-0036

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title = "Extension of the unit normal vector field from a hypersurface",

abstract = "In many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.",

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author = "Roland Duduchava and Eugene Shargorodsky and George Tephnadze",

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T1 - Extension of the unit normal vector field from a hypersurface

AU - Duduchava, Roland

AU - Shargorodsky, Eugene

AU - Tephnadze, George

PY - 2015/9

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N2 - In many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.

AB - In many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.

KW - extended normal vector field

KW - Hypersurface

KW - proper extension

KW - unit normal vector field

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DO - 10.1515/gmj-2015-0036

M3 - Article

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VL - 22

SP - 355

EP - 359

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 3

ER -

Extension of the unit normal vector field from a hypersurface

Abstract

Keywords

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