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2015•Georgian Mathematical JournalRequires access

Extension of the unit normal vector field from a hypersurface

Roland Duduchava, Eugene Shargorodsky, George Tephnadze

Open publisher page 6 citations

Abstract

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.

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Method / approach

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Available abstract

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.

Key concepts: Hypersurface, Extension (predicate logic), Mathematics, Vector field, Unit (ring theory), Unit vector, Uniqueness, Field (mathematics)

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