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Remarks on Kähler Ricci Flow
, 2009
"... We show the convergence of Kähler Ricci flow directly if the αinvariant of the canonical class is greater than n n+1. Applying these convergence theorems, we can give a Kähler Ricci flow proof of Calabi conjecture on such Fano manifolds. In particular, the existence of KE metrics on a lot of Fano s ..."
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Cited by 3 (0 self)
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We show the convergence of Kähler Ricci flow directly if the αinvariant of the canonical class is greater than n n+1. Applying these convergence theorems, we can give a Kähler Ricci flow proof of Calabi conjecture on such Fano manifolds. In particular, the existence of KE metrics on a lot of Fano
(KÄHLER)RICCI FLOW ON (KÄHLER) MANIFOLDS
"... One of the most interesting questions in Riemannian geometry is that of deciding whether a manifold admits curvatures of certain kinds. More specifically, one might want to know whether some given manifold admits a canonical metric, i.e. one with constant curvature of some ..."
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One of the most interesting questions in Riemannian geometry is that of deciding whether a manifold admits curvatures of certain kinds. More specifically, one might want to know whether some given manifold admits a canonical metric, i.e. one with constant curvature of some
Ricci flows and their integrability in two dimensions
 C. R. Phys
"... We review the main aspects of Ricci flows as they arise in physics and mathematics. In field theory they describe the renormalization group equations of the target space metric of two dimensional sigma models to lowest order in the perturbative expansion. As such they provide an offshell approach t ..."
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Cited by 2 (0 self)
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We review the main aspects of Ricci flows as they arise in physics and mathematics. In field theory they describe the renormalization group equations of the target space metric of two dimensional sigma models to lowest order in the perturbative expansion. As such they provide an offshell approach
RICCI FLOW, QUANTUM MECHANICS AND GRAVITY
, 808
"... Abstract It has been argued that, underlying any given quantum–mechanical model, there exists at least one deterministic system that reproduces, after prequantisation, the given quantum dynamics. For a quantum mechanics with a complex d–dimensional Hilbert space, the Lie group SU(d) represents class ..."
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classical canonical transformations on the projective space CP d−1 of quantum states. Let R stand for the Ricci flow of the manifold SU(d − 1) down to one point, and let P denote the projection from the Hopf bundle onto its base CP d−1. Then the underlying deterministic model we propose here is the Lie
Kähler Ricci flow on Fano surfaces (I)
, 2007
"... We show the convergence of Kähler Ricci flow on toric Fano surfaces staring from any Kähler metric in the canonical class. ..."
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Cited by 1 (0 self)
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We show the convergence of Kähler Ricci flow on toric Fano surfaces staring from any Kähler metric in the canonical class.
The Ricci iteration and its applications
, 706
"... Abstract. In this note we introduce and study dynamical systems related to the Ricci operator on the space of Kähler metrics as discretizations of certain geometric flows. We pose a conjecture on their convergence towards canonical Kähler metrics and provide a proof in the case the first Chern class ..."
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Abstract. In this note we introduce and study dynamical systems related to the Ricci operator on the space of Kähler metrics as discretizations of certain geometric flows. We pose a conjecture on their convergence towards canonical Kähler metrics and provide a proof in the case the first Chern
MINIMALLY INVASIVE SURGERY FOR RICCI FLOW SINGULARITIES
"... Abstract. In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on S n+1, without performing an intervening surgery. In the restrictive context of rotational symmetry, this construction gives evidence in favor o ..."
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Cited by 15 (2 self)
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of Perelman’s hope for a “canonically defined Ricci flow through singularities”. Contents
Nonholonomic Ricci flows. II. Evolution equations and dynamics
 J. Math. Phys
"... This is the second paper in a series of works devoted to nonholonomic Ricci flows. Following our idea that imposing non–integrable (nonholonomic) constraints on Ricci flows of Riemannian metrics, we model mutual transforms of generalized Finsler–Lagrange and Riemann geometries. There are verified so ..."
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Cited by 19 (18 self)
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some assertions made in the first partner paper and developed a formal scheme in which the geometric constructions are elaborated for the canonical nonlinear and linear connections. The scheme is applied to a study of Hamilton’s Ricci flows on nonholonomic manifolds and related Einstein spaces
Results 11  20
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1,556