The structure of continuous rigid functions of two variables

Details The structure of continuous rigid functions of two variables The structure of continuous rigid functions of two variables

2011-09-22

arxiv.org/abs/1109.4951v1

Real Anal. Exchange 35 (2009), no. 1, 139-156

Mathematics

Classical Analysis and ODEs

Scientific paper

A function $f:\RR^n \to \RR$ is called \emph{vertically rigid} if $graph(cf)$ is isometric to $graph (f)$ for all $c \neq 0$. We settled Jankovi\'c's conjecture in a separate paper by showing that a continuous function $f:\RR \to \RR$ is vertically rigid if and only if it is of the form $a+bx$ or $a+be^{kx}$ ($a,b,k \in \RR$). Now we prove that a continuous function $f:\RR^2 \to \RR$ is vertically rigid if and only if after a suitable rotation around the z-axis $f(x,y)$ is of the form $a + bx + dy$, $a + s(y)e^{kx}$ or $a + be^{kx} + dy$ ($a,b,d,k \in \RR$, $k \neq 0$, $s : \RR \to \RR$ continuous). The problem remains open in higher dimensions.

Affiliated with

Also associated with

No associations

Rating

The structure of continuous rigid functions of two variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The structure of continuous rigid functions of two variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The structure of continuous rigid functions of two variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-723777