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955
Harmonic maps between noncompact manifolds
 J. Nonlinear Math. Phys
"... We describe the problem of finding a harmonic map between noncompact manifold. Given some sufficient conditions on the domain, the target and the initial map, we prove the existence of a harmonic map that deforms the given map. 1 ..."
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Cited by 1 (0 self)
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We describe the problem of finding a harmonic map between noncompact manifold. Given some sufficient conditions on the domain, the target and the initial map, we prove the existence of a harmonic map that deforms the given map. 1
Uniqueness of the Ricci flow on complete noncompact manifolds
, 2005
"... The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton [8]. Later on, De Turck [4] gave a simplified proof. In the later of 80’s, Shi [20] generalized the local existence result t ..."
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Cited by 54 (5 self)
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to complete noncompact manifolds. However, the uniqueness of the solutions to the Ricci flow on complete noncompact manifolds is still an open question. Recently it was found that the uniqueness of the Ricci flow on complete noncompact manifolds is important in the theory of the Ricci flow with surgery
Uniqueness of solutions of Ricci flow on complete noncompact manifolds
"... Abstract. We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow on complete noncompact manifolds with bounded curv ..."
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Cited by 8 (6 self)
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Abstract. We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow on complete noncompact manifolds with bounded
Noncompact manifolds with nonnegative Ricci curvature
 J. Geom. Anal
"... Let (M, d) be a metric space. For 0 < r < R, let G(p,r, R) be the group obtained by considering all loops based at a point p∈M whose image is contained in the closed ball of radius r and identifying two loops if there is a homotopy betweeen them that is contained in the open ball of radius R. ..."
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Cited by 5 (1 self)
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. In this paper we study the asymptotic behavior of the G(p,r, R) groups of complete open manifolds of nonnegative Ricci curvature. We also find relationships between the G(p,r, R) groups and tangent cones at infinity of a metric space and show that any tangent cone at infinity of a complete open manifold
Fixedpoint theories on noncompact manifolds
 JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
, 2009
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Some constructions for the fractional Laplacian on noncompact manifolds
"... We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by CaffarelliSilvestre. While this definition in the compact case is straightforward, in the noncompact setting one needs to have a precise control of the behavior of the metric at ..."
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Cited by 6 (0 self)
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We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by CaffarelliSilvestre. While this definition in the compact case is straightforward, in the noncompact setting one needs to have a precise control of the behavior of the metric
Gradient and Harnack inequalities on noncompact manifolds with boundary
 Pacific Journal of Math
"... By using the reflecting diffusion process and a conformal change of metric, a generalized maximum principle is established for (unbounded) timespace functions on a class of noncompact Riemannian manifolds with (nonconvex) boundary. As applications, Li–Yautype gradient and Harnack inequalities are ..."
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Cited by 6 (2 self)
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By using the reflecting diffusion process and a conformal change of metric, a generalized maximum principle is established for (unbounded) timespace functions on a class of noncompact Riemannian manifolds with (nonconvex) boundary. As applications, Li–Yautype gradient and Harnack inequalities
CALIBRATED FIBRATIONS ON NONCOMPACT MANIFOLDS VIA GROUP ACTIONS
"... In this paper we use Lie group actions on noncompact Riemannian manifolds with calibrations to construct calibrated submanifolds. In particular, if we have an (n−1)torus acting on a noncompact CalabiYau nfold with a trivial first cohomology, then we have a special Lagrangian fibration on that nfo ..."
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Cited by 9 (0 self)
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In this paper we use Lie group actions on noncompact Riemannian manifolds with calibrations to construct calibrated submanifolds. In particular, if we have an (n−1)torus acting on a noncompact CalabiYau nfold with a trivial first cohomology, then we have a special Lagrangian fibration on that n
Results 1  10
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955