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Tytuł artykułu

On the Curvature and Heat Flow on Hamiltonian Systems

Autorzy

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

Słowa kluczowe

Wydawca

Rocznik

Tom

2

Numer

1

Opis fizyczny

Daty

wydano
2014-01-01
otrzymano
2013-08-20
zaakceptowano
2014-02-14
online
2014-04-24

Twórcy

  • Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

Bibliografia

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  • [4] A. A. Agrachev and P. W. Y. Lee, Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds, Preprint (2009). Available at arXiv:0903.2550
  • [5] A. A. Agrachev and P.W. Y. Lee, Bishop and Laplacian comparison theorems on three dimensional contact subriemannian manifolds with symmetry, to appear in J. Geom. Anal. Available at arXiv:1105.2206
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  • [28] M. Kell, On interpolation and curvature via Wasserstein geodesics, Preprint (2013). Available at arXiv:1311.5407
  • [29] M. Kell, q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space, Preprint (2014). Available at arXiv:1401.0840
  • [30] P. W. Y. Lee, A remark on the potentials of optimal transport maps, Acta Appl. Math. 115 (2011), 123-138.
  • [31] P. W. Y. Lee, Displacement interpolations from a Hamiltonian point of view, J. Funct. Anal. 265 (2013), 3163-3203.
  • [32] P. W. Y. Lee, C. Li and I. Zelenko, Measure contraction properties of contact sub-Riemannian manifolds with symmetry, Preprint (2013). Available at arXiv:1304.2658
  • [33] J. Lott and C. Villani, Weak curvature conditions and functional inequalities, J. Funct. Anal. 245 (2007), 311-333.
  • [34] J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2) 169 (2009), 903-991.
  • [35] J. Maas, Gradient flows of the entropy for finite Markov chains, J. Funct. Anal. 261 (2011), 2250-2292.
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  • [46] S. Ohta and K.-T. Sturm, Bochner-Weitzenböck formula and Li-Yau estimates on Finslermanifolds, Adv.Math. 252 (2014), 429-448.
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  • [54] Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Adv. Math. 128 (1997), 306-328.
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  • [56] K.-T. Sturm, On the geometry of metric measure spaces. I, Acta Math. 196 (2006), 65-131.
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  • [59] G. Wang and C. Xia, A sharp lower bound for the first eigenvalue on Finsler manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), 983-996.
  • [60] G. Wei and W. Wylie, Comparison geometry for the Bakry-Emery Ricci tensor, J. Differential Geom. 83 (2009), 377-405.
  • [61] C. Xia, Local gradient estimate for harmonic functions on Finsler manifolds, to appear in Calc. Var. Partial Differential Equations. Available at arXiv:1308.3609

Typ dokumentu

Bibliografia

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Identyfikator YADDA

bwmeta1.element.doi-10_2478_agms-2014-0003
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