000			04951nam a22004813i 4500
001			EBC6118470
003			MiAaPQ
005			20240724114122.0
006			m o d |
007			cr cnu||||||||
008			240724s2019 xx o ||||0 eng d
020			_a9781470455132 _q(electronic bk.)
020			_z9781470439132
035			_a(MiAaPQ)EBC6118470
035			_a(Au-PeEL)EBL6118470
035			_a(OCoLC)1140400914
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA611.28 _b.A437 2019
082	0		_a514.32000000000005
100	1		_aAmbrosio, Luigi.
245	1	0	_aNonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2019.
264		4	_c©2019.
300			_a1 online resource (134 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.262
505	0		_aCover -- Title page -- Chapter 1. Introduction -- Chapter 2. Contraction and Convexity via Hamiltonian Estimates: an Heuristic Argument -- Part I . Nonlinear Diffusion Equations and Their Linearization in Dirichlet Spaces -- Chapter 3. Dirichlet Forms, Homogeneous Spaces and Nonlinear Diffusion -- 3.1. Dirichlet forms -- 3.2. Completion of quotient spaces w.r.t. a seminorm -- 3.3. Nonlinear diffusion -- Chapter 4. Backward and Forward Linearizations of Nonlinear Diffusion -- Part II . Continuity Equation and Curvature Conditions in Metric Measure Spaces -- Chapter 5. Preliminaries -- 5.1. Absolutely continuous curves, Lipschitz functions and slopes -- 5.2. The Hopf-Lax evolution formula -- 5.3. Measures, couplings, Wasserstein distance -- 5.4. _{ }-absolutely continuous curves and dynamic plans -- 5.5. Metric measure spaces and the Cheeger energy -- 5.6. Entropy estimates of the quadratic moment and of the Fisher information along nonlinear diffusion equations -- 5.7. Weighted Γ-calculus -- Chapter 6. Absolutely Continuous Curves in Wasserstein Spaces and Continuity Inequalities in a Metric Setting -- Chapter 7. Weighted Energy Functionals along Absolutely Continuous Curves -- Chapter 8. Dynamic Kantorovich Potentials, Continuity Equation and Dual Weighted Cheeger Energies -- Chapter 9. The \RCDS Condition and Its Characterizations through Weighted Convexity and Evolution Variational Inequalities -- 9.1. Green functions on intervals -- 9.2. Entropies and their regularizations -- 9.3. The \CDS condition and its characterization via weighted action convexity -- 9.4. \RCD ∞ spaces and a criterium for \CDS via -- Part III . Bakry-Émery Condition and Nonlinear Diffusion -- Chapter 10. The Bakry-Émery Condition -- 10.1. The Bakry-Émery condition for local Dirichlet forms and interpolation estimates.
505	8		_a10.2. Local and "nonlinear" characterization of the metric \BE condition in locally compact spaces -- Chapter 11. Nonlinear Diffusion Equations and Action Estimates -- Chapter 12. The Equivalence Between \BE and \RCDS -- 12.1. Regular curves and regularized entropies -- 12.2. \BE yields for regular entropy functionals in \MC -- 12.3. \RCDS implies \BE -- Bibliography -- Back Cover.
520			_aThe aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,\mathsf d,\mathfrak m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong \mathrm {CD}^{*}(K,N) condition of Bacher-Sturm.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aMetric spaces.
655		4	_aElectronic books.
700	1		_aMondino, Andrea.
700	1		_aSavaré, Giuseppe.
776	0	8	_iPrint version: _aAmbrosio, Luigi _tNonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces _dProvidence : American Mathematical Society,c2019 _z9781470439132
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6118470 _zClick to View
999			_c16243 _d16243