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Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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has standard geometry. The point is to make h arbitrarily small while keeping r bounded away from zero. Notation and terminology B(x, t, r) denotes the open metric ball of radius r, with respect to the metric at time t, centered at x. P(x, t, r, △t) denotes a parabolic neighborhood, that is the set
εNEIGHBORHOODS OF ORBITS AND FORMAL CLASSIFICATION OF PARABOLIC DIFFEOMORPHISMS
"... Abstract. In this article we study the dynamics generated by germs of parabolic diffeomorphisms f: (C, 0) → (C, 0) tangent to the identity. We show how formal classification of a given parabolic diffeomorphism can be deduced from the asymptotic development of what we call directed area of the εnei ..."
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Abstract. In this article we study the dynamics generated by germs of parabolic diffeomorphisms f: (C, 0) → (C, 0) tangent to the identity. We show how formal classification of a given parabolic diffeomorphism can be deduced from the asymptotic development of what we call directed area of the εneighborhood
εNEIGHBORHOODS OF ORBITS OF PARABOLIC DIFFEOMORPHISMS AND COHOMOLOGICAL EQUATIONS
"... Abstract. In this article, we study analyticity properties of (directed) areas of εneighborhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using εneighborhoods of orbits in the simplest formal class. We show that the coefficient in front of ..."
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Abstract. In this article, we study analyticity properties of (directed) areas of εneighborhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using εneighborhoods of orbits in the simplest formal class. We show that the coefficient in front
parabolic fixed points
"... This note is a summary of the $\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{r}\dot{\mathrm{i}}\mathrm{t}[8]$. We will show that the Fatou coordinates (the solution to Abel equation) for a parabolic fixed point of holomorphic map of one variable can be obtained as a modified limit of the solution ..."
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This note is a summary of the $\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{r}\dot{\mathrm{i}}\mathrm{t}[8]$. We will show that the Fatou coordinates (the solution to Abel equation) for a parabolic fixed point of holomorphic map of one variable can be obtained as a modified limit of the solution
SMALL PERTURBATION SOLUTIONS FOR PARABOLIC EQUATIONS
"... Abstract. Let ϕ be a smooth solution of the parabolic equation F (D2u,Du, u, x, t) − ut = 0. Assume that F is smooth and uniformly elliptic only in a neighborhood of the points (D2ϕ,Dϕ,ϕ, x, t), we show that a viscosity solution u to the above equation is smooth in the interior if ‖u − ϕ‖L ∞ is suf ..."
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Cited by 1 (0 self)
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Abstract. Let ϕ be a smooth solution of the parabolic equation F (D2u,Du, u, x, t) − ut = 0. Assume that F is smooth and uniformly elliptic only in a neighborhood of the points (D2ϕ,Dϕ,ϕ, x, t), we show that a viscosity solution u to the above equation is smooth in the interior if ‖u − ϕ
Isolated Singularities of Nonlinear Parabolic Inequalities
"... We study C 2,1 nonnegative solutions u(x, t) of the nonlinear parabolic inequalities 0 ≤ ut − ∆u ≤ u λ in a punctured neighborhood of the origin in R n × [0, ∞), when n ≥ 1andλ>0. We show that a necessary and sufficient condition on λ for such solutions u to satisfy an a priori bound near the ori ..."
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Cited by 3 (2 self)
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We study C 2,1 nonnegative solutions u(x, t) of the nonlinear parabolic inequalities 0 ≤ ut − ∆u ≤ u λ in a punctured neighborhood of the origin in R n × [0, ∞), when n ≥ 1andλ>0. We show that a necessary and sufficient condition on λ for such solutions u to satisfy an a priori bound near
A parabolic twophase obstaclelike equation
 Adv. Math
"... Abstract. For the parabolic obstacleproblemlike equation ∆u − ∂tu = λ+χ{u>0} − λ−χ{u<0}, where λ+ and λ − are positive Lipschitz functions, we prove in arbitrary finite dimension that the free boundary ∂{u> 0} ∪ ∂{u < 0} is in a neighborhood of each “branch point ” the union of two L ..."
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Cited by 9 (3 self)
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Abstract. For the parabolic obstacleproblemlike equation ∆u − ∂tu = λ+χ{u>0} − λ−χ{u<0}, where λ+ and λ − are positive Lipschitz functions, we prove in arbitrary finite dimension that the free boundary ∂{u> 0} ∪ ∂{u < 0} is in a neighborhood of each “branch point ” the union of two
Holomorphic motions, Fatou linearization, and quasiconformal rigidity for parabolic germs
, 2007
"... By applying holomorphic motions, we prove that a parabolic germ is quasiconformally rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller ..."
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Cited by 4 (3 self)
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By applying holomorphic motions, we prove that a parabolic germ is quasiconformally rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller
Parabolic Problems with Nonlinear Boundary Conditions in Cell Tissues 1
"... Abstract: In this paper we consider reaction diffusion problems with nonlinear boundary conditions in two dimensional domains for which the diffusion is large except in a neighborhood of a one dimensional set where it becomes small. We regard the domain as a cell tissue. The cell tissue is divided ..."
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Abstract: In this paper we consider reaction diffusion problems with nonlinear boundary conditions in two dimensional domains for which the diffusion is large except in a neighborhood of a one dimensional set where it becomes small. We regard the domain as a cell tissue. The cell tissue is divided
Global nonnegative controllability of the semilinear parabolic equation governed by bilinear control
, 2002
"... We study the global approximate controllability of the one dimensional semilinear convectiondiusionreaction equation governed in a bounded domain via the coecient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not ..."
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Cited by 5 (3 self)
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that can be steered in L²(0; 1) from any nonnegative nonzero initial state into any neighborhood of any desirable nonnegative target state by at most three static (xdependent only) abovementioned bilinear controls, applied subsequently in time, while only one such control is needed in the linear case.
Results 1  10
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63