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Search Results: 1 - 10 of 793 matches for " Kota Hattori "
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The volume growth of hyperkaehler manifolds of type A_{\infty}
Kota Hattori
Mathematics , 2010,
Abstract: We study the volume growth of hyperkaehler manifolds of type $A_{\infty}$ constructed by Anderson-Kronheimer-LeBrun and Goto. These are noncompact complete 4-dimensional hyperkaehler manifolds of infinite topological type. These manifolds have the same topology but the hyperkaehler metrics are depends on the choice of parameters. By taking a certain parameter, we show that there exists a hyperkaehler manifold of type $A_{\infty}$ whose volume growth is r^a for each 3
The holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}
Kota Hattori
Mathematics , 2012,
Abstract: We study the holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}, by using the torus action.
A generalization of Taub-NUT deformations
Kota Hattori
Mathematics , 2013,
Abstract: We introduce a generalization of Taub-NUT deformations for large families of hyper-Kaehler quotients including toric hyper-Kaehler manifolds and quiver varieties, and apply them to the case of the Hilbert schemes of k points on C^2.
A rigidity theorem for quaternionic Kaehler structures
Kota Hattori
Mathematics , 2008,
Abstract: We study the moduli space of quaternionic Kaehler structures on a compact manifold of dimension 4n (n>2) from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kaehler structures of nonzero scalar curvature by observing the moduli space.
New examples of compact special Lagrangian submanifolds embedded in hyper-K?hler manifolds
Kota Hattori
Mathematics , 2014,
Abstract: We construct smooth families of compact special Lagrangian submanifolds embedded in some toric hyper-K\"ahler manifolds, which never become holomorphic Lagrangian submanifolds via any hyper-K\"ahler rotations. These families converge to special Lagrangian immersions with self-intersection points in the sense of current. To construct them, we apply the desingularization method developed by Joyce.
The nonuniqueness of the tangent cone at infinity of Ricci-flat manifolds
Kota Hattori
Mathematics , 2015,
Abstract: It is shown by Colding and Minicozzi the uniqueness of the tangent cone at infinity of Ricci-flat manifolds with Euclidean volume growth which has at least one tangent cone at infinity with a smooth cross section. In this article we raise an example of the Ricci-flat manifold implying that the assumption for the volume growth in the above result is essential. More precisely, we construct a complete Ricci-flat manifold of dimension 4 with non-Euclidean volume growth who has at least two distinct tangent cones at infinity and one of them has a smooth cross section.
Self-similar solutions to the mean curvature flows on Riemannian cone manifolds and special Lagrangians on toric Calabi-Yau cones
Akito Futaki,Kota Hattori,Hikaru Yamamoto
Mathematics , 2011,
Abstract: The self-similar solutions to the mean curvature flows have been defined and studied on the Euclidean space. In this paper we initiate a general treatment of the self-similar solutions to the mean curvature flows on Riemannian cone manifolds. As a typical result we extend the well-known result of Huisken about the asymptotic behavior for the singularities of the mean curvature flows. We also extend the results on special Lagrangian submanifolds on $\mathbb C^n$ to the toric Calabi-Yau cones over Sasaki-Einstein manifolds.
An integral invariant from the view point of locally conformally K?hler geometry
Akito Futaki,Kota Hattori,Liviu Ornea
Mathematics , 2011,
Abstract: In this paper we study an integral invariant which obstructs the existence on a compact complex manifold of a volume form with the determinant of its Ricci form proportional to itself, in particular obstructs the existence of a K\"ahler-Einstein metric, and has been studied since 1980's. We study this invariant from the view point of locally conformally K\"ahler geometry. We first see that we can define an integral invariant for coverings of compact complex manifolds with automorphic volume forms. This situation typically occurs for locally conformally K\"ahler manifolds. Secondly, we see that this invariant coincides with the former one. We also show that the invariant vanishes for any compact Vaisman manifolds.
Mechanical effects of surgical procedures on osteochondral grafts elucidated by osmotic loading and real-time ultrasound
Koji Hattori, Kota Uematsu, Tomohiro Matsumoto, Hajime Ohgushi
Arthritis Research & Therapy , 2009, DOI: 10.1186/ar2801
Abstract: A full-thickness cylindrical osteochondral defect (diameter, 3.5 mm; depth, 5 mm) was created in the lateral lower quarter of the patella. Using graft-harvesting instruments, an osteochondral plug (diameter, 3.5 mm as exact-size or 4.5 mm as oversize; depth, 5 mm) was harvested from the lateral upper quarter of the patella and transplanted into the defect. Intact patella was used as a control. The samples were monitored by real-time ultrasound during sequential changes of the bathing solution from 0.15 M to 2 M saline (shrinkage phase) and back to 0.15 M saline (swelling phase). For cartilage sample assessment, three indices were selected, namely the change in amplitude from the cartilage surface (amplitude recovery rate: ARR) and the maximum echo shifts from the cartilage surface and the cartilage-bone interface.The ARR is closely related to the cartilage surface integrity, while the echo shifts from the cartilage surface and the cartilage-bone interface are closely related to tissue deformation and NaCl diffusion, respectively. The ARR values of the oversized plugs were significantly lower than those of the control and exact-sized plugs. Regarding the maximum echo shifts from the cartilage surface and the cartilage-bone interface, no significant differences were observed among the three groups.These findings demonstrated that osmotic loading and real-time ultrasound were able to assess the mechanical condition of cartilage plugs after osteochondral grafting. In particular, the ARR was able to detect damage to the superficial collagen network in a non-destructive manner. Therefore, osmotic loading and real-time ultrasound are promising as minimally invasive methods for evaluating cartilage damage in the superficial zone after trauma or impact loading for osteochondral grafting.Osteochondral grafts have become popular for the treatment of small, isolated and full-thickness cartilage lesions [1]. Osteochondral grafts have several advantages, including a high survival
Spectrocolorimetric assessment of cartilage plugs after autologous osteochondral grafting: correlations between color indices and histological findings in a rabbit model
Koji Hattori, Kota Uematsu, Yohei Tanikake, Takashi Habata, Yasuhito Tanaka, Hiroshi Yajima, Yoshinori Takakura
Arthritis Research & Therapy , 2007, DOI: 10.1186/ar2287
Abstract: Although articular cartilage shows durability and the ability to maintain itself, it has limited capacity for repair [1,2]. The repair cartilage that forms as a result of articular injury has a different structure from hyaline cartilage and exhibits inferior mechanical properties and wear characteristics. Thus, once damage has occurred, it continues to accumulate, eventually leading to complete loss of the articular surface and exposure of the underlying bone. These changes are almost always associated with severely impaired joint function and clinical symptoms of redness, swelling and pain [1,3,4]. Therefore, the poor quality of cartilage repair tissue has led surgeons to develop procedures intended to improve articular cartilage repair, thereby improving joint function and decreasing joint pain. Several surgical techniques are currently used in clinical practice, namely debridement, microfracture, drilling, abrasion arthroplasty, autologous osteochondral grafting (OCG) and cultured autologous chondrocyte transplantation [3-7].OCG has become popular as a means for treating articular cartilage defects [5,8]. This technique involves transplantation of osteochondral plugs from a non-weightbearing region to the defect lesion. OCG has several advantages over other surgical treatments for articular cartilage defects. Specifically, OCG is currently the only technique able to fill a joint surface defect with hyaline cartilage, is a relatively simply method compared with autologous chondrocyte transplantation, shows little immunological rejection and is disease-free. However, 5% to 20% of the procedures fail overtly, and several authors have noted the presence of fibrillation or fibrocartilage formation in patients on later histological examination [8-11]. Fibrillation or conversion to fibrocartilage is considered undesirable because these tissues are less smooth and less stiff than normal cartilage and may tend to slough over time. However, the fibrous overgrowth is grossl
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