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Citations Publications citing this paper. Submanifolds in carnot groups Davide Vittone.

On the Obata Theorem in a weighted Sasakian manifold. Treu , Davide Vittone. Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups Francesco Serra Cassano , Davide Vittone.

Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group Donatella Danielli , Nunzia Garofalo , D. Nhieu , Scott D. References Publications referenced by this paper.

Structural inequalities method for uniqueness theorems for the minimal surface equation Jenn-Fang Hwang. Ricci flow, simplicial volume, and smooth structures Masashi Ishida Sophia University Abstract It is conjectured by Fuquan Fang, Yuguang Zhang and Zhenlei Zhang that the existence of non-singular solutions to the normalized Ricci flow on smooth closed 4-manifolds with non-trivial Gromov's simplicial volume and negative Perelman's invariant implies the Gromov-Hitchin-Thorpe type inequality. This conjecture is still open.

In this talk, we shall discuss the existence of closed topological 4-manifolds with non-trivial Gromov's simplicial volume and satisfying the Gromov-Hitchin-Thorpe type inequality, but admitting infinitely many exotic smooth structures for which Perelman's invariant is negative and there is no non-singular solution to the normalized Ricci flow for any initial metric.


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In particular, the main result of this talk tells us that the converse of the conjecture dose not hold in general. We use the Seiberg-Witten monopole equations to prove the main result.

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The symplectic volume of the space was studied by many mathematicians using various approaches. I will survey these researches. A rough equivalence among partial differential equations Tsuyoshi Kato Kyoto University Abstract Real hypersurfaces in a complex space form and the generalized Tanaka-Webster connection Mayuko Kon Hokkaido University Abstract In this talk I will present the results for the curvature tensor and the Ricci tensor with respect to the generalized Tanaka-Webster connection of a real hypersurface in a complex space form. The generalized Tanaka-Webster connection for a real hypersurfaces of Kaehlerian manifolds was studied by J.

It coincids with the Tanaka-Webster connection if the associated CR-structure of the real hypersurface is pseudo-Hermitian and strongly pseudo-convex. In the special case when the Riemannian manifold is locally conformally flat, the result reduces to the well-known result.

This generalizes the famous Eells-Sampson's theorem. On Lagrangian submanifolds in complex hyperquadrics Hui Ma Tsinghua University Abstract The Gauss map of any oriented isoparametric hypersurface of the sphere defines a minimal Lagrangian submanifold in the complex hyperquadric. In this talk, we determine the Hamiltonian stability of ALL compact minimal Lagrangian submanifolds embedded in complex hyperquadrics obtained as the Gauss images of homogeneous isoparametric hypersurfaces in spheres.

The relation between the Gauss image construction and the conormal bundle construction for Lagrangian submanifolds in complex hyperquadrics will also be discussed. This talk is mainly based on the joint work with Professor Yoshihiro Ohnita. The moduli space of transverse Calabi-Yau structures on foliated manifolds Takayuki Moriyama Kyoto University Abstract We develop a moduli theory of transverse structures given by closed forms on foliated manifolds.

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We show that the moduli space of transverse Calabi-Yau structures is a Hausdorff and smooth manifold if the foliation is taut. In this talk, we will give some examples of transverse Calabi-Yau structures on foliated manifolds. Wave equations and the LeBrun-Mason twistor correspondence Fuminori Nakata Tokyo Institute of Technology Abstract Invariant geometric flows and integrable systems Changzheng Qu Northwest University Abstract In this talk, we shall discuss the relationship between invariant geometric flows and integrable systems. It is shown that many integrable systems are associated with the invariant geometric flows in some geometries.

The geometric interpretation to properties of integrable systems such as the Backlund transformation, Miura transformation and bi-Hamiltonian structure etc are given in terms of the geometric flows. Firstly, some Finslerian type models introduced in ecology, and secondly, the so-called Kosambi-Cartan-Chern theory. The second topic is a Finslerian alternative to the classical notion of Lyapunov stability of dynamical systems and it is used in various fields of the science nowadays.

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It will be important to study geometric solutions of PDEs. Tangle analysis of site-specific recombination Koya Shimokawa Saitama University Abstract Action of site-specific recombinase can be analysed using tangle model introduced by Ernst and Sumners. In this talk we apply this method and give topological characterizations of actions of several site-specific recombinases. We can identify the parts of the more complex organisms, and know that these parts are sometimes exchangeable by grafting or transplantation.