User christian - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T07:36:55Z http://mathoverflow.net/feeds/user/17463 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75331/decompose-a-set-into-sets-of-hausdorff-dimension-n-1 Decompose a set into sets of Hausdorff-dimension n-1 Christian 2011-09-13T16:40:14Z 2011-09-13T17:24:55Z <p>Assume we can decompose a set $A$ in $\mathbb{R^n}$ of Hausdorff-dimension n into sets $(A_t)$ $t\in [0,1]$ of Hausdorff-dimension n-1 whose n-1-dimensional volume is known (for example is zero). </p> <p>Are there any possibilities beside the coarea-formula that allow us to say something about the measure of A?</p> http://mathoverflow.net/questions/73978/geodesics-intersecting-a-submanifold Geodesics intersecting a submanifold Christian 2011-08-29T15:54:31Z 2011-08-30T06:48:16Z <p>Let $U$ be an open subset in $R^n$ and let $N$ be a $C^1$-submanifold. We have a family of geodesics $\gamma:[0,1]\rightarrow U$ in U with respect to the euclidian metric. Each geodesic is parametrized with constant speed and and intersects with $N$ in exactly one point $\gamma(\tau(\gamma))$. We have $sup_{t\in [0,1]}|\gamma(t),\tilde{\gamma}(t)|\leq C|\gamma(0),\tilde{\gamma}(0)|$ for all $\gamma$ and $\tilde{\gamma}$ and C is a constant.</p> <p>Is the map $\gamma(0)\mapsto\gamma(\tau(\gamma))$ Lipschitz?</p> http://mathoverflow.net/questions/73978/geodesics-intersecting-a-submanifold/73987#73987 Comment by Christian Christian 2011-08-30T07:00:21Z 2011-08-30T07:00:21Z Ok, :-) thank you http://mathoverflow.net/questions/73978/geodesics-intersecting-a-submanifold Comment by Christian Christian 2011-08-29T21:17:01Z 2011-08-29T21:17:01Z Would the statement be true if we assume that the intersections are transversal and replace Lipschitz by locally Lipschitz?