Titles and Short Summaries of the Talks

31 Geometry
Final: 2013/2/7
26 Shun Maeta (Tohoku Univ.) ♯ Biharmonic Lagrangian submanifolds in complex space forms · · · · · · · · 10
Hajime Urakawa (Tohoku Univ.)
Summary: We give the necessary and sufficient conditions for Lagrangian submanifolds in Kähler
manifolds to be biharmonic. We classify biharmonic PNMC Lagrangian H-umbilical submanifolds
in the complex space forms. Furthermore, we classify biharmonic PNMC Lagrangian surfaces in
the 2-dimensional complex space forms.
27 Yoshio Matsuyama (Chuo Univ.) ♯ Curvature pinching for complete submanifolds · · · · · · · · · · · · · · · · · · · · · 10
Summary: Complete classifications for a complete Kaehler submanifold Mn with the scalar
curvature ρ ≥ n 2 in a complex projective space and for a complete totally real minimal submanifold
with nonnegative sectional curvature in a complex projective space are given, so that a conjecture
of K. Ogiue are resolved.
28 Hiroki Sako (Kyoto Univ.) ∗ Generalizations of expander graphs and Property A for discrete metric
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: I will introduce a generalization of expander sequences. An expander sequence is finite
graphs which are highly connected in some sence. A sequence of weighted weak expander spaces
will be defined. I will also review several notions related to amenability for discrete groups and
metric spaces. Property A can be regarded as amenability for discrete metric spaces. It is proved
that for a metric space X the following are equivalent: (i) there exists a sequence of weighted weak
expander spaces inside X, (ii) X does not have property A.
29 Shouhei Honda (Kyushu Univ.) ∗ A Bochner type inequality on limit spaces. · · · · · · · · · · · · · · · · · · · · · · · · 20
Summary: We give the definition of L p -convergence of tensor fields with respect to the Gromov–
Hausdorff topology and several fundamental properties of the convergence. We apply this to
establish a Bochner-type inequality which keeps the term of Hessian on the Gromov–Hausdorff limit
space of a sequence of Riemannian manifolds with a lower Ricci curvature bound and to give a
geometric explicit formula for the Dirichlet Laplacian on a limit space defined by Cheeger–Colding.
30 Kei Kondo (Tokai Univ.) ♯ Toponogov’s comparison theorem in Finsler geometry · · · · · · · · · · · · · · · 20
Shin-ichi Ohta (Kyoto Univ.)
Minoru Tanaka (Tokai Univ.)
Summary: We recently established a Toponogov comparison theorem for Finsler manifolds, in the
manner of radial curvature geometry. Here, we consider the situation that the radial flag curvature
is bounded below by the radial curvature function of a non-compact surface of revolution, the edge
opposite to the base point is contained in a Berwald-like region, and that the Finsler metric is
convex enough in the radial directions in that region.