User yves - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T06:28:42Z http://mathoverflow.net/feeds/user/27061 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109055/integral-inequality-involving-the-biharmonic-operator Integral inequality involving the biharmonic operator Yves 2012-10-07T12:25:50Z 2012-10-07T19:42:31Z <p>Let M be a hyperbolic surface and let f be a real smooth function on M.</p> <p>Considering a geometric inequality which I conjectured to be true for different reasons, I get after a lot of computations that the inequality is in fact equivalent to the following </p> <p>$$\int_{M}(f^2 - \frac{1}{4}(Delta(f))^2)dMâ‰¤ \frac{1}{V}(\int_{M}fdM)^2$$,</p> <p>where dm is the volume form on M and $V=\int_{M}dM$.</p> <p>Is this inequality correct or false ?</p> http://mathoverflow.net/questions/109055/integral-inequality-involving-the-biharmonic-operator Comment by Yves Yves 2012-10-07T19:02:56Z 2012-10-07T19:02:56Z But if you scale the metric, you change the curvature (by hyperbolic, I mean &quot;constant curvature equal to -1&quot;). http://mathoverflow.net/questions/109055/integral-inequality-involving-the-biharmonic-operator Comment by Yves Yves 2012-10-07T16:14:43Z 2012-10-07T16:14:43Z I apologize: the notation was unclear. Thank you.