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SHORT GEODESIC LOOPS ON COMPLETE RIEMANNIAN MANIFOLDS WITH A FINITE VOLUME
, 2013
"... In this paper we will show that on any complete noncompact Riemannian manifold with a finite volume there exist uncountably many geodesic loops of arbitrarily small length. ..."
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In this paper we will show that on any complete noncompact Riemannian manifold with a finite volume there exist uncountably many geodesic loops of arbitrarily small length.
New gap theorem on complete Riemannian manifolds ∗
, 2006
"... In this short note, we find a new gap phenomena on Riemannian manifolds, which says that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the scalar curvature decays faster than quadratically, then it is Ricci flat. ..."
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In this short note, we find a new gap phenomena on Riemannian manifolds, which says that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the scalar curvature decays faster than quadratically, then it is Ricci flat.
© Printed in India Estimates and nonexistence of solutions of the scalar curvature equation on noncompact manifolds
, 2004
"... Abstract. This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions of sc ..."
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Abstract. This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions
On the spectrum of the LaplaceBeltrami operator for pforms on asymptotically hyperbolic manifolds
 Rend. Accad. Naz. Sci. XL Mem. Math. Appl. (2002) Vol. XXVI
"... The spectrum of the LaplaceBeltrami operator on complete noncompact Riemannian manifolds in its connections with the geometrical properties has been investigated by many authors; however, they have mainly studied the case of scalar functions, whilst less is known about ..."
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Cited by 7 (1 self)
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The spectrum of the LaplaceBeltrami operator on complete noncompact Riemannian manifolds in its connections with the geometrical properties has been investigated by many authors; however, they have mainly studied the case of scalar functions, whilst less is known about
Positively Curved Complete Noncompact Kähler Manifolds
, 2002
"... In this paper we give a partial affirmative answer to a conjecture of GreeneWu and Yau. We prove that a complete noncompact Kähler surface with positive and bounded sectional curvature and with finite analytic Chern number c1(M) 2 is biholomorphic to C 2. The celebrated theorem of Cheeger–Gromoll–M ..."
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–Gromoll–Meyer [3], [10] states that a complete noncompact Riemannian manifold with positive sectional curvature is diffeomorphic to the Euclidean space. It is wellknown that there is a vast variety of biholomorphically distinct complex structures on R 2n for n> 1 ( see
HAMILTON’S GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR FAST DIFFUSION EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS
"... (Communicated by ChuuLian Terng) Abstract. Let M be a complete noncompact Riemannian manifold of dimension n. In this paper, we derive a local gradient estimate for positive solutions of fast diffusion equations ∂tu =Δu α, 1 − 2 n <α<1 on M × (−∞, 0]. We also obtain a theorem of Liouville typ ..."
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(Communicated by ChuuLian Terng) Abstract. Let M be a complete noncompact Riemannian manifold of dimension n. In this paper, we derive a local gradient estimate for positive solutions of fast diffusion equations ∂tu =Δu α, 1 − 2 n <α<1 on M × (−∞, 0]. We also obtain a theorem of Liouville
Theorem 1. (Castañeda 98) Let (M, g) be a
"... We consider nonsymmetric diffusion operators on complete noncompact Riemannian manifolds. L =∆+X ∆ = the LaplaceBeltrami operator X = is a vector field. We analyze positive solutions of Lu = 0 ..."
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We consider nonsymmetric diffusion operators on complete noncompact Riemannian manifolds. L =∆+X ∆ = the LaplaceBeltrami operator X = is a vector field. We analyze positive solutions of Lu = 0
A NOTE ON RICCI FLOW ON COMPLETE 3MANIFOLDS
, 807
"... Abstract. Let (M 3, g0) be a complete noncompact Riemannian manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature R(x) → 0 as x → ∞. Then the Ricci flow with initial data (M 3, g0) has a longtime solution. This extends a rec ..."
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Abstract. Let (M 3, g0) be a complete noncompact Riemannian manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature R(x) → 0 as x → ∞. Then the Ricci flow with initial data (M 3, g0) has a longtime solution. This extends a
GRADIENT ESTIMATES FOR A NONLINEAR PARABOLIC EQUATION ON RIEMANNIAN MANIFOLDS
"... Abstract. Let (M, g) be a complete noncompact Riemannian manifold. In this paper, we derive a local gradient estimate for positive solutions to a simple nonlinear parabolic equation ∂u =∆u+ au log u + bu ∂t on M × [0, +∞), where a, b are two real constants. This equation is closely related to the gr ..."
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Abstract. Let (M, g) be a complete noncompact Riemannian manifold. In this paper, we derive a local gradient estimate for positive solutions to a simple nonlinear parabolic equation ∂u =∆u+ au log u + bu ∂t on M × [0, +∞), where a, b are two real constants. This equation is closely related
Results 1  10
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