M. V. Korobkov, “An example of a <nobr>$C^1$</nobr>-smooth function whose gradient range is an arc with no tangent at any point”, Sibirsk. Mat. Zh., 2008, Volume 49, Number 1,Pages <nobr>134

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An example of a $C^1$-smooth function whose gradient range is an arc with no tangent at any point

M. V. Korobkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We construct an example of a $C^1$-smooth real function of two variables whose gradient range is an arc with no tangent at any point.

Keywords: $C^1$-smooth function, gradient range, arc, tangent.

UDC: 517.95

Received: 02.02.2006