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Title: Sharp estimates of the mean field equations at critical parameters
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Abstract:
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Takanari Saotome (Institute of Mathematics, Academia Sinica, NTU) |
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Title: Some Estimates for a Solution to CR Yamabe Equation |
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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. |
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Miyuki Koiso（IMI, Kyushu University, Japan) |
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Title: Non-convex anisotropic surface energy and zero mean curvature surfaces
in the Lorentz-Minkowski space
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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).
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Ryoichi Kobayashi（Nagoya University, Japan) |
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Title: Hamiltonian volume minimizing property of $U(1)^n$-orbits in $CP^n$
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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 $\{\phi(T_t)\}$.
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| Shin Nayatani（Nagoya University, Japan) |
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Title: Fixed-Point Property of Infinite Groups |
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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).
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Katrin Leschke
(University of Leicester, UK) |
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Title: Quaternionic Holomorphic Geometry: transformations of minimal surfaces |
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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 joint work with K. Moriya (University of Tsukuba).
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Katsuhiro Moriya（University of Tsukuba, Japan) |
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Title: Surfaces with vanishing Willmore energy in Euclidean four-space |
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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.
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Kensuke Onda（Nagoya University & OCAMI, Japan) |
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Title: Algebraic Ricci solitons on Lorentzian Lie groups
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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.
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Hitoshi Yamanaka（Osaka City University, Japan) |
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Title: Hyperbolic diffeomorphisms and representation coverings |
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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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