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FN ISI Export Format VR 1.0 PT J AU Kebekus, S Kovacs, SJ AF Kebekus, Stefan Kovacs, Sandor J. TI Families of canonically polarized varieties over surfaces SO INVENTIONES MATHEMATICAE AB Shafarevich's hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In this paper, we relate the variation of a family to the logarithmic Kodaira dimension of the base and give an affirmative answer to Viehweg's conjecture for families parametrized by surfaces. C1 Univ Cologne, Math Inst, D-50931 Cologne, Germany. Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Kebekus, S, Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany. EM stefan.kebekus@math.uni-koeln.de kovacs@math.washington.edu PD JUN PY 2008 VL 172 IS 3 BP 657 EP 682 UT ISI:000255113800007 ER PT J AU Colton, D Paivarinta, L Sylvester, J AF Colton, David Paeivaerinta, Lassi Sylvester, John TI The interior transmission problem SO INVERSE PROBLEMS AND IMAGING AB The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations. This paper presents old and new results for the interior transmission problem, in particular its relation to inverse scattering theory and new results on the spectral theory associated with this class of boundary value problems. C1 Univ Delaware, Dept Math Sci, Newark, DE 19716 USA. Univ Helsinki, Dept Math & Stat, Helsinki, Finland. Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Colton, D, Univ Delaware, Dept Math Sci, Newark, DE 19716 USA. EM colton@math.udel.edu lassi.paivarinta@helsinki.fi sylvest@math.washington.edu PD FEB PY 2007 VL 1 IS 1 BP 13 EP 28 UT ISI:000255070500003 ER PT J AU Heck, H Uhlmann, G Wang, JN AF Heck, Horst Uhlmann, Gunther Wang, Jenn-Nan TI Reconstruction of obstacles immersed in an incompressible fluid SO INVERSE PROBLEMS AND IMAGING AB We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokes equation with a variable viscosity. C1 Tech Univ Darmstadt, FB Math, AG 4, D-64289 Darmstadt, Germany. Univ Washington, Dept Math, Seattle, WA 98195 USA. Natl Taiwan Univ, Dept Math, TIMS, Taipei 106, Taiwan. Natl Taiwan Univ, Dept Math, CTS Taipei, Taipei 106, Taiwan. RP Heck, H, Tech Univ Darmstadt, FB Math, AG 4, Schlossgartenstr 7, D-64289 Darmstadt, Germany. EM heck@mathematik.tu-darmstadt.de gunther@math.washington.edu jnwang@math.ntu.edu.tw PD FEB PY 2007 VL 1 IS 1 BP 63 EP 76 UT ISI:000255070500006 ER PT J AU Nadirashvili, N Yuan, Y AF Nadirashvili, Nikolai Yuan, Yu TI Improving Pogorelov's isometric embedding counterexample SO CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS AB We construct a C (2,1) metric of non-negative Gauss curvature with no C-2 local isometric embedding in R-3. C1 Univ Washington, Dept Math, Seattle, WA 98195 USA. Ctr Math & Informat, LATP, F-13453 Marseille, France. RP Yuan, Y, Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA. EM nicolas@cmi.univ-mrs.fr yuan@math.washington.edu PD JUL PY 2008 VL 32 IS 3 BP 319 EP 323 UT ISI:000255031500002 ER EF
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