most recent 30 from http://mathoverflow.net 2013-05-21T16:51:05Z http://mathoverflow.net/feeds/question/56056 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56056/tangent-surfaces-curvature-inequality Beni Bogosel 2011-02-20T11:49:49Z 2011-02-20T11:49:49Z

<p>I found this lemma in a few surface geometry proofs:</p> <p>If we have two surfaces, $S$ and $S'$, which are tangent in the point $p$ then if: (i) $S'$ has positive curvature in $p$; (ii) $S$ is, locally around $p$, situated on the same side of $S'$, then the curvature of $S$ in $p$ is greater or equal to the curvature of $S'$ in $p$.</p> <p>I am interested in a book/reference where I can find a proof for this lemma. Thank you.</p>