# Differential Geometry and Geometric Analysis

 DateF March 25 (Mon)- March 27 (Wed), 2013 PlaceF Lecture Room 301, General Research Building (No. 29) , Department of Mathematics, Graduate School of Science, Osaka City University

 OrganizersF Shu-Cheng Chang (NTU & TIMS), Chang-Shou Lin (NTU, TIMS Director), Martin Guest (Waseda University & Visiting Pprofessor of OCAMI), Akio Kawauchi (OCU, OCAMI Director), Yoshihiro OhnitaiOCU, OCAMI Vice-directorj

 SponsorsF Osaka City University Advanced Mathematical Institute (OCAMI). @ National Taiwan University (NTU), Taida Institute for Mathematical Sciences @ @ @

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 Invited speakersF Professor Shu-Cheng Chang (National Taiwan University, Taiwan) Professor Chen-Yu Chi (National Taiwan University, Taiwan) Professor Hsin-Yuan Huang (National Sun Yat-sen University, Taiwan) Professor Chiung-Ju Liu iNational Taiwan University, Taiwan) Professor Chin-Lung Wang (National Taiwan University, Taiwan) Doctor Ting-Jung Kuo (Taida Institute for Mathematical Sciences, NTU, Taiwan) Doctor Takanari Saotome (Institute of Mathematics, Academia Sinica, Taiwan) Professor Miyuki Koiso iInstitute of Mathematics for Industry IMI, Kyushu University, Japan) Professor Ryoichi Kobayashi iNagoya University, Japan) Professor Shin NayataniiNagoya University, Japan) Professor Katrin Leschke (University of Leicester, UK) Doctor Katsuhiro Moriya iUniversity of Tsukuba, Japan) Doctor Kensuke Onda iNagoya University & OCAMI, Japan) Mr. Hitoshi Yamanaka iPh.D. student, Osaka City University, Japan) etc.

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 Title and Abstract of Talks F abstract (in preparation) Shu-Cheng Chang (National Taiwan University, Taiwan) Title: The torsion flow in a closed strictly pseudoconvex CR 3-manifold Abstract: In this talk, we define the torsion flow, a CR analogue of the Ricci flow. We first show that the torsion flow has short time existence for suitable initial conditions in a closed strictly pseudoconvex CR 3-manifold. Secondly, we give some examples for the long-time solution of the torsion flow. Finally, we derive monotonicity formulas for CR Perlman-type entropy functionals. As an application, we classify the torsion breathers. This is a jointed work with Otto van Koert and Chin-Tung Wu. Chen-Yu Chi (National Taiwan University, Taiwan) Title: On Toda systems of VHS type with singular sources Abstract: We consider the Toda systems of VHS type with singular sources and provide a criterion for the existence of solutions with prescribed asymptotic behaviour near singularities when all the singular strengths are integral multiples of $n+1$, where $n$ is the number of equations in the system. We also prove the uniqueness of solution for general assignments of singular strengths. Our approach uses Simpson's theory of constructing Higgs-Hermitian-Yang-Mills metrics from stability. Hsin-Yuan Huang (National Sun Yat-sen University, Taiwan) Title: On the Entire Radial Solutions of the Chern-Simons SU(3) System Abstract: In this talk, we study the entire radial solutions of the self-dual equations arising from the relativistic SU(3) Chern-Simons model proposed by Kao-Lee and Dunne. Understanding the structure of entire radial solutions is one of fundamental issues for the system of nonlinear equations. In this paper, we prove any entire radial solutions must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at in finity of these solutions. Even for radial solutions, this classification has remained an open problem for many years. As an application of this classification, we prove that the two components u and v have intersection at most finite times. This is joint work with Chang-Shou Lin. Chiung-Ju Liu (National Taiwan University, Taiwan) Title: The asymptotic expansion of Tian-Yau-Zelditch on Riemann surfaces Abstract: In this talk, we will learn about the asymptotic expansion of Tian-Yau-Zelditch on polarized Kahler manifolds and discuss its behavior on Riemann surfaces with -1 constant scalar curvature. Chin-Lung Wang (National Taiwan University, Taiwan) Title: Mean field equations and algebraic geometry Abstract: In this talk I will discuss a correspondence between non-linear mean field equations on flat tori (PDE), generalized Lame equations (ODE), and certain polynomial systems (algebraic geometry). In particular this correspondence enables us to count the number of mean field solutions using algebraic geometry. Also the notion of analytic degeneracy and algebraic degeneracy match perfectly. This is a joint work with Ching-Li Chai and Chang-Shou Lin. Ting-Jung Kuo (Taida Institute for Mathematical Sciences, NTU) Title: Sharp estimates of the mean field equations at critical parameters Abstract: PDF Takanari Saotome (Institute of Mathematics, Academia Sinica, NTU) Title: Some Estimates for a Solution to CR Yamabe Equation Abstract: In this talk, we study some inequalities for solutions to CR Yamabe equation. This study is motivated from the study of the moduli space of the solutions to the Yamabe equation. This is a joint work with Professor Jhi-Hsin Cheng. @@@ Miyuki KoisoiIMI, Kyushu University, Japan) Title: Non-convex anisotropic surface energy and zero mean curvature surfaces in the Lorentz-Minkowski space Abstract: We study stationary surfaces of anisotropic surface energies in the euclidean three-space which are called anisotropic minimal surfaces. Usual minimal surfaces, zero mean curvature spacelike surfaces and timelike surfaces in the Lorenz-Minkowski space are regarded as anisotropic minimal surfaces for certain special axisymmetric anisotropic surface energies. In this talk, for any axisymmetric anisotropic surface energy, we show that, a surface is both a minimal surface and an anisotropic minimal surface if and only if it is a right helicoid. We also construct new examples of anisotropic cyclic minimal surfaces for certain reasonable classes of energy density. Our examples include zero mean curvature timelike surfaces and spacelike surfaces of catenoid-type and Riemann- type. This is a joint work with Atsufumi Honda (Tokyo Institute of Technology). Ryoichi KobayashiiNagoya University, Japan) Title: Hamiltonian volume minimizing property of $U(1)^n$-orbits in $CP^n$ Abstract: We will prove that any maximal dimensional $U(1)^n$-orbit in $CP^n$ is volume minimizing under Hamiltonian deformation. The idea of the proof is the following : (1) We extend a given $U(1)^n$-orbit to the moment torus fibration $\{T_t\}$ and consider its Hamiltonian deformation $\{\phi(T_t)\}$ where $\phi$ is a Hamiltonian diffeomorphism of $CP^n$. Then (2) We compare a given $U(1)^n$-orbit and its Hamiltonian deformation by looking at the large $k$-asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis $H^0(CP^n,O(k))$ obtained by Borthwick-Paul-Uribe semi-classical approximation of the $k$-Bohr-Sommerfeld tori of the Lagrangian torus fibration $\{T_t\}$ and its Hamiltonian deformation $\{\phi(T_t)\}$. Shin NayataniiNagoya University, Japan) Title: Fixed-Point Property of Infinite Groups Abstract: I'll make a small survey on geometric approach to superrigidity and fixed-point property (fpp) of infinite groups. Starting form the fpp of individual groups, I'll discuss the fpp of random groups, and then the monstrous groups of Gromov. This talk is based on the joint work with Hiroyasu Izeki (Keio) and Takefumi Kondo (Tohoku). @@@ Katrin Leschke (University of Leicester, UK) Title: Quaternionic Holomorphic Geometry: transformations of minimal surfaces Abstract: There are various harmonic maps which are canonically associated to a minimal surface, e.g., the Gauss map of the immersion and the conformal Gauss map. Using methods from Quaternionic Holomorphic Geoemtry, we will discuss how the well-known dressing operation on harmonic maps applied to the associated harmonic maps of a minimal surface is related to transformations on the minimal surface. In particular, we will show that the simple factor dressing is connected to a generalised associated family and a family of Willmore surfaces given by the minimal surface. This is a joint work with K. Moriya (University of Tsukuba). Katsuhiro MoriyaiUniversity of Tsukuba, Japan) Title: Surfaces with vanishing Willmore energy in Euclidean four-space Abstract: We regard a conformal map from a Riemann surface to Euclidean four-space with vanishing Willmore energy as a higher codimensional version of a holomorphic function or a meromorphic funciton. Then we find a property of a surface with vanishing Willmore energy by a similar way to find a property of a holomorphic function or a meromorphic function. Kensuke OndaiNagoya University & OCAMI, Japan) Title: Algebraic Ricci solitons on Lorentzian Lie groups Abstract: Ricci solitons have been intensively studied. The concept of the algebraic Ricci soliton was first introduced by Lauret in Riemannian case. Algebraic Ricci soliton is useful for studying Ricci solitons on homogeneous manifolds. In this talk, we study algebraic Ricci solitons on Lorentzian Lie groups. Hitoshi YamanakaiOsaka City University, Japan) Title: Hyperbolic diffeomorphisms and representation coverings Abstract: For a given invariant hyperbolic diffeomorphism satisfying a certain convergence condition, We show a Morse theoretic analogue of a theorem of Bialynicki-Birula concerning the existence of invariant Zariski open coverings. We also discuss about the converse of the above result in case of holomorphic torus actions.

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Program F program (in preparation)

 3/25iMonj AM 9:30-10:00 Lecture Room 301 Registration and Opening AM 10:00-10:50 Lecture Room 301 Ryoichi Kobayashi AM 11:10-12:00 Lecture Room 301 Chin-Lung Wang PM 13:30-14:20 Lecture Room 301 Chen-Yu Chi PM 14:30-15:20 Lecture Room 301 Miyuki Koiso PM 15:30- Free Discussion @@ 3/26iTuej AM 9:30-10:20 Lecture Room 301 Kensuke Onda AM 10:30-11:20 Lecture Room 301 Ting-Jung Kuo AM 11:30-12:20 Lecture Room 301 Hsin-Yuan Huang PM 14:00-14:50 Lecture Room 301 Chiung-Ju Liu PM 15:00-15:40 Lecture Room 301 Hitoshi Yamanaka PM 16:00-16:40 Lecture Room 301 Katrin Leschke PM 16:50-17:30 Lecture Room 301 Katsuhiro Moriya 3/27iWedj AM 9:30-10:20 Lecture Room 301 Shu-Cheng Chang AM 10:30-11:20 Lecture Room 301 Shin Nayatani AM 11:30-12:20 Lecture Room 301 Takanari Saotome PM 13:40-14:30 Lecture Room 301 @@@

Suggestion to Speakers :

At the lecture room there are enough blackboards, the computer projector and the visualizer. Please prepare your talk using them.

Notice F This workshop is held as one of joint activities under the agreement of academic cooperation between TIMS and OCAMI.

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 LinkF Osaka City University Advanced Mathematical Institute (OCAM I) Department of Mathematics, Osaka City Univercity National Taiwan University Taida Institute for Mathematical Sciences (TIMS) TIMS One-Day Workshop on Differential Geometry (April 1, 2008) The 1st OCAMI-TIMS Joint International Workshop on Differential Geometry and Geomtric Analysis (March 9-10, 2009) The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geomtric Analysis (March 21-23, 2010) Poster The 3rd OCAMI-TIMS Joint International Workshop on Differential Geometry and Geomtric Analysis (March 13-15, 2011) The 4th TIMS-OCAMI Joint International Workshop on Differential Geometry and Geomtric Analysis (March 17-19, 2012) Poster Kansai Kenshu Center (KKC)

 SupportF JSPS Grant-in-Aid for Scientific Research (A) No.21244004 "Construction of new relationship of differential geometry and quantum cohomology by integrable systems" (Principal investigaor: Martin Guest)

Contactie-mailj
Yoshihiro OhnitaF ohnita (at) sci.osaka-cu.ac.jp

̂ Last updated on 1/March/2013