Gunhee Cho

     Speaker Gunhee Cho UCSB We seek to gain progress on the following long-standing conjectures in hyperbolic complex geometry: prove that a simply connected complete Kähler manifold with negatively pinched sectional curvature is biholomorphic to a bounded domain and the Carathéodory-Reiffen metric does not vanish everywhere. As the next development of the important recent …

    Speaker Gunhee Cho UCSB By exploiting the upper semicontinuity of the Kobayashi-Eisenman pseudo volume (and pseudometric) under deformations of complex structures, we establish the non-measure hyperbolicity of K3 surfaces—which M. Green and P. Griffiths verified for certain cases in 1980—holds for all K3 surfaces. Our result provides a stronger condition than the Kobayashi …