Zobrazeno 1 - 10
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pro vyhledávání: '"Takashi SHIOYA"'
Autor:
Takashi Shioya
Publikováno v:
Sugaku Expositions. 35:221-241
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e6fc133d6654d26576d0f1c02e98a1fe
https://doi.org/10.1090/suga/475
https://doi.org/10.1090/suga/475
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete,
Autor:
Hiroki Nakajima, Takashi Shioya
Publikováno v:
Advances in Mathematics. 349:1198-1233
We prove that if a geodesic metric measure space satisfies a comparison condition for isoperimetric profile and if the observable variance is maximal, then the space is foliated by minimal geodesics, where the observable variance is defined to be the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85893538e7a17b11baa814c096480afa
https://doi.org/10.1016/j.aim.2019.04.043
https://doi.org/10.1016/j.aim.2019.04.043
Autor:
Takashi Shioya, Asuka Takatsu
Publikováno v:
Mathematische Zeitschrift. 290:873-907
We study the high-dimensional limit of (projective) Stiefel and flag manifolds as metric measure spaces in Gromov’s topology. The limits are either the infinite-dimensional Gaussian space or its quotient by some mm-isomorphic group actions, which a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04dcca82d8606d8bed17a10e87506868
https://doi.org/10.1007/s00209-018-2044-y
https://doi.org/10.1007/s00209-018-2044-y
Autor:
Koji Fujiwara, Takashi Shioya
Publikováno v:
Geom. Topol. 24, no. 4 (2020), 2035-2074
Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which is an "eve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d6de8d382491a210dd543f547a7e34d5
http://arxiv.org/abs/1903.07216
http://arxiv.org/abs/1903.07216
Autor:
Ryunosuke Ozawa, Takashi Shioya
Publikováno v:
Manuscripta Mathematica. 147:501-509
We estimate the observable diameter of the $l_p$-product space $X^n$ of an mm-space $X$ by using the limit formula in our previous paper. The idea of our proof is based on Gromov's book. As a corollary we obtain the phase transition property of $\{X^
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d6f761aca9910adc09dc439cebe4172
https://doi.org/10.1007/s00229-015-0730-1
https://doi.org/10.1007/s00229-015-0730-1
Autor:
Takashi Shioya
Publikováno v:
Measure Theory in Non-Smooth Spaces ISBN: 9783110550832
We study the limits of sequences of spheres and complex projective spaces with unbounded dimensions. A sequence of spheres (resp. complex projective spaces) either is a Levy family, infinitely dissipates, or converges to (resp. the Hopf quotient of)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::94c83c6918a7db1cddda5c957e0aafd7
https://doi.org/10.1515/9783110550832-009
https://doi.org/10.1515/9783110550832-009
Autor:
Takashi Shioya, Kei Funano
Publikováno v:
Geometric and Functional Analysis. 23:888-936
In this paper we study the concentration behavior of metric measure spaces. We prove the stability of the curvature-dimension condition with respect to the concentration topology due to Gromov. As an application, under the nonnegativity of Bakry–Em
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::31d0dd8b5c8ed15ae3f15e51d998d2b0
https://doi.org/10.1007/s00039-013-0215-x
https://doi.org/10.1007/s00039-013-0215-x
Autor:
Takashi Shioya
Publikováno v:
IRMA Lectures in Mathematics and Theoretical Physics ISBN: 9783037191583
In this book, we study Gromov's metric geometric theory on the space of metric measure spaces, based on the idea of concentration of measure phenomenon due to Levy and Milman. Although most of the details are omitted in the original article of Gromov
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::788da609ec58888730bfdcbbcea6e68b
https://doi.org/10.4171/158
https://doi.org/10.4171/158
Autor:
Takashi Shioya
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9784431560197
We survey some parts of Gromov’s theory of metric measure spaces [6, Sect. 3.\(\frac{1}{2}\)], and report our recent works [14, 15, 16, 17], focusing on the asymptotic behavior of a sequence of spaces with unbounded dimension.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f65af5a0142c0586f09a9cdb958803e4
https://doi.org/10.1007/978-4-431-56021-0_16
https://doi.org/10.1007/978-4-431-56021-0_16