What is the analog of "monotonic" for scalar functions on surfaces? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T19:07:13Z http://mathoverflow.net/feeds/question/94576 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94576/what-is-the-analog-of-monotonic-for-scalar-functions-on-surfaces What is the analog of "monotonic" for scalar functions on surfaces? mangledorf 2012-04-19T21:29:57Z 2012-06-01T02:56:05Z <p>"monotonic" is well defined for functions $f(x)$, where e.g. $x\in[0,1]$ and $f(x)\in\mathbb{R}$. The quality I particularly care about is that if $f(x)$ is monotonic then it will not have any local extrema for $x\in(0,1)$.</p> <p>Is there an analogous word for a function $g(x,y)$ with $x,y\in[0,1]$ and $g(x,y)\in\mathbb{R}$, where $g(x,y)$ has no local extrema for $x,y\in(0,1)$?</p>