http://imrn.oxfordjournals.org International Mathematics Research Notices - RSS feed of current issue 1687-0247 2009 International Mathematics Research Notices 1073-7928 http://imrn.oxfordjournals.org/cgi/content/short/2009/13/i?rss=1 2009-06-28 info:doi/10.1093/imrn/rnp097 Oxford University Press 13 2009 i 2009-06-28 i TOC http://imrn.oxfordjournals.org/cgi/content/short/2009/13/ii?rss=1 2009-06-28 info:doi/10.1093/imrn/rnp098 Oxford University Press 13 2009 ii 2009-06-28 ii Subscriptions http://imrn.oxfordjournals.org/cgi/content/short/2009/13/iii?rss=1 2009-06-28 info:doi/10.1093/imrn/rnp106 Oxford University Press 13 2009 iii 2009-06-28 iii Editors http://imrn.oxfordjournals.org/cgi/content/short/2009/13/2347?rss=1 We prove that no curvature-dimension bound CD(K,N) holds in any Heisenberg group . On the contrary, the measure contraction property MCP(0, 2n + 3) holds and is optimal for the dimension 2n + 3. For the nonexistence of a curvature-dimension bound, we prove that the generalized "geodesic" Brunn–Minkowski inequality is false in . We also show in a new and direct way (and for all ), that the general "multiplicative" Brunn–Minkowski inequality with dimension N > 2n + 1 is false.

]]> 2009-06-28 info:doi/10.1093/imrn/rnp019 Oxford University Press 13 2009 2373 2009-06-28 2347 Article http://imrn.oxfordjournals.org/cgi/content/short/2009/13/2374?rss=1 We determine the fusion rules for the minimal series representations over the super-Virasoro algebras including the Ramond sector.

]]> 2009-06-28 info:doi/10.1093/imrn/rnp020 Oxford University Press 13 2009 2416 2009-06-28 2374 Article http://imrn.oxfordjournals.org/cgi/content/short/2009/13/2417?rss=1 Our purpose is to make a contribution to the foundation of the theory of formal scheme. We are interested particularly in non-Noetherian or non-adic formal schemes, which have been little studied. We redefine the formal scheme as a proringed space and study its basic properties. We also find several examples of non-adic formal schemes.

]]> 2009-06-28 info:doi/10.1093/imrn/rnp021 Oxford University Press 13 2009 2475 2009-06-28 2417 Article http://imrn.oxfordjournals.org/cgi/content/short/2009/13/2476?rss=1 We prove some simple special cases, partly new, of results of André–Oort–Manin–Mumford type using an extension to algebraic points of bounded degree of a result of Pila–Wilkie on the density of rational points on sets definable in an o-minimal structure. The strategy follows that of a recent new proof of the Manin–Mumford conjecture by Pila–Zannier, and a proof of a special (but new) case of Pink's relative Manin–Mumford conjecture by Masser–Zannier.

]]> 2009-06-28 info:doi/10.1093/imrn/rnp022 Oxford University Press 13 2009 2507 2009-06-28 2476 Article http://imrn.oxfordjournals.org/cgi/content/short/2009/13/2508?rss=1 In this paper, we consider the viscous n-dimensional Camassa–Holm equations in the whole space. Various regularity criteria for the strong solution are established. As a corollary, we show the existence of a global smooth solution when .

]]> 2009-06-28 info:doi/10.1093/imrn/rnp023 Oxford University Press 13 2009 2518 2009-06-28 2508 Article http://imrn.oxfordjournals.org/cgi/content/short/2009/13/2519?rss=1 We calculate the matrix of the Frobenius map on the middle-dimensional cohomology of the one-parameter family that is related by mirror symmetry to the family of all quintic threefolds.

]]> 2009-06-28 info:doi/10.1093/imrn/rnp024 Oxford University Press 13 2009 2545 2009-06-28 2519 Article