Gunhee Cho, Non-measure Hyperbolicity of K3 and Enriques Surfaces

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 non-hyperbolicity for any complex K3 surface, which had been demonstrated by L. Kamenova, S. Lu, and M. Verbitsky. An interesting consequence is the non-measure hyperbolicity of Enriques surfaces. This is the joint work with David R. Morrison.