Convexity of a cone in CxC - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T00:54:06Z http://mathoverflow.net/feeds/question/60834 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/60834/convexity-of-a-cone-in-cxc Convexity of a cone in CxC nonameisfinetoo 2011-04-06T16:41:57Z 2011-04-06T16:41:57Z <p>Hi. I have trouble deciding if the set of couples $\left( \xi, \zeta \right) \in \mathbb{C}^2$ with $Re \left( \xi \text{ } \overline{\zeta} \right) > 0$ is convex. It is a (real) cone, but is it a convex one? If not, could you provide me with a counter-example?</p> <p>thx.</p>