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Bounded Manifold Completion
[article]

2019
*
arXiv
*
pre-print

In this paper, we will present a thematically different approach to detect the existence of a low-dimensional

arXiv:1912.09026v1
fatcat:hr2v7yuxdzednhxj3zkduzxwkq
*manifold*of a given dimension that lies within a set of*bounds*derived from a given point cloud ... set of fully observed entries that can be implemented as a low-rank Matrix*Completion*(MC) problem. ... Therefore, we name our method*Bounded**Manifold**Completion*(BMC). ...##
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Complete manifolds with bounded curvature and spectral gaps
[article]

2017
*
arXiv
*
pre-print

We study the spectrum of

arXiv:1510.05046v2
fatcat:dxahimnl75c67jx6wnm4rpyl3y
*complete*noncompact*manifolds*with*bounded*curvature and positive injectivity radius. ... Also, for any*complete*noncompact*manifold*with*bounded*curvature and positive injectivity radius we construct a metric uniformly equivalent to the given one (also of*bounded*curvature and positive injectivity ... Each of these will be a*complete*non-compact*manifold*with*bounded*curvature and positive injectivity radius. ...##
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Density of bounded maps in Sobolev spaces into complete manifolds

2017
*
Annali di Matematica Pura ed Applicata
*

Given a

doi:10.1007/s10231-017-0664-1
fatcat:fccjxrv6yjdj7kbszm45tnz2ji
*complete*noncompact Riemannian*manifold*N^n, we investigate whether the set of*bounded*Sobolev maps (W^1, p∩ L^∞) (Q^m; N^n) on the cube Q^m is strongly dense in the Sobolev space W^1, p (Q^m; ... The proof is*complete*.*Bounded*maps Let N n be an (abstract)*complete*Riemannian*manifold*. ... The proof of Proposition 3.3 relies on the next lemma which allows one to identify a*bounded*map into a*complete**manifold*as a map into a compact*manifold*. ...##
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Bounded harmonic $1$-forms on complete manifolds

2008
*
Proceedings of the American Mathematical Society
*

In this paper we present some results concerning

doi:10.1090/s0002-9939-08-09645-7
fatcat:6ygsexsyknecdcoukktvzzlxne
*bounded*harmonic 1-forms on*manifolds*of compact type. ... As a corollary we obtain a rigidity result for the first cohomology group of locally isometric Riemannian*manifolds*. ... If f is a*bounded*harmonic function w.r.t. g, then f is a constant. Definition 1.3. Let M be a*complete*Riemannian*manifold*. ...##
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Remark on a diameter bound for complete manifolds with positive Bakry-Émery Ricci curvature
[article]

2015
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arXiv
*
pre-print

In this paper, we shall give a new upper diameter estimate for

arXiv:1504.05384v2
fatcat:xxt2bttzcffqvjxud6lpnuzeyu
*complete*Riemannian*manifolds*in the case that the Bakry-\'Emery Ricci curvature has a positive lower*bound*and the norm of the potential ... function has an upper*bound*. ... Introduction Let (M, g) be a*complete*Riemannian*manifold*and f : M → R a smooth function. ...##
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Extension of holomorphic canonical forms on complete d-bounded Kahler manifolds
[article]

2020
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arXiv
*
pre-print

In this paper we study the extension of holomorphic canonical forms on

arXiv:2004.13246v1
fatcat:auyup3ncpjdovivdacpm5wa4q4
*complete*d-*bounded*Kahler*manifolds*by using L2 analytic methods and L2 Hogde theory, which generalizes some classical results to ... Let (X, ω) be a*complete*d-*bounded*Kähler*manifold*of dimension n. ... This*completes*the proof. Let (X, ω) be a*complete*d-*bounded*Kähler*manifold*of dimension n. ...##
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TOPOLOGY OF COMPLETE FINSLER MANIFOLDS WITH RADIAL FLAG CURVATURE BOUNDED BELOW

2014
*
Kyushu Journal of Mathematics
*

We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler

doi:10.2206/kyushujm.68.347
fatcat:r4xd5eehdvd6fhhn7zn4zxkgy4
*manifolds*whose radial flag curvatures are*bounded*below by that of a von Mangoldt surface of revolution ... Let (M, F, p) be a forward*complete*, non-compact, connected C ∞ -Finsler*manifold*whose radial flag curvature is*bounded*below by that of a von Mangoldt surface ( � M,p) satisfying f � (ρ) = 0 and G(ρ) ... Let (M, F, p) be a forward*complete*, non-compact, connected C ∞ -Finsler*manifold*whose radial flag curvature is*bounded*below by that of a von Mangoldt surface ( � M,p) satisfying f � (ρ) = 0 and G(ρ) ...##
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Complete manifolds with bounded curvature and spectral gaps

2016
*
Journal of Differential Equations
*

We study the spectrum of

doi:10.1016/j.jde.2016.05.002
fatcat:tjk6gptilnenfkg5k6rkpzr4dm
*complete*noncompact*manifolds*with*bounded*curvature and positive injectivity radius. ... Also, for any*complete*noncompact*manifold*with*bounded*curvature and positive injectivity radius we construct a metric uniformly equivalent to the given one (also of*bounded*curvature and positive injectivity ... Each of these will be a*complete*non-compact*manifold*with*bounded*curvature and positive injectivity radius. ...##
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Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
[article]

2016
*
arXiv
*
pre-print

, to this class of noncompact

arXiv:1404.3245v3
fatcat:v74xhiqxkrevnmwdnifsjvji24
*complete*Riemannian*manifolds*with*bounded*geometry. ... For a*complete*noncompact connected Riemannian*manifold*with*bounded*geometry M^n, we prove that the isoperimetric profile function I_M^n is continuous. ... This*completes*the proof. q.e.d. Figure 1 . 1 Let M be a Riemannian*manifold*(possibly incomplete, or possibly*complete*not necessarily with*bounded*geometry). ...##
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Weak approximation by bounded Sobolev maps with values into complete manifolds

2018
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Comptes rendus. Mathematique
*

We have recently introduced the trimming property for a

doi:10.1016/j.crma.2018.01.017
fatcat:xlpkghvncrbh3jn3jfj4de5uzm
*complete*Riemannian*manifold*N^n as a necessary and sufficient condition for*bounded*maps to be strongly dense in W^1, p(B^m; N^n) when p ∈{1, , ... We prove in this note that even under a weaker notion of approximation, namely the weak sequential convergence, the trimming property remains necessary for the approximation in terms of*bounded*maps. ... In a recent work [5] , we have considered the question of what happens when the target*manifold*N n is not compact, but merely*complete*. ...##
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Poincaré inequality on complete Riemannian manifolds with Ricci curvature bounded below
[article]

2018
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arXiv
*
pre-print

We prove that

arXiv:1801.04216v1
fatcat:3j4p6nxt75ez3gcsueazzl3rre
*complete*Riemannian*manifolds*with polynomial growth and Ricci curvature*bounded*from below, admit uniform Poincaré inequalities. ... A global, uniform Poincaré inequality for horospheres in the universal cover of a closed, n-dimensional Riemannian*manifold*with pinched negative sectional curvature follows as a corollary. ... Let (M n , g) be a*complete*Riemannian*manifold*satisfying the Ricci curvature*bound*(0.1) and the α-polynomial growth assumption (0.2). ...##
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Density and non-density of C^∞_c ↪ W^k,p on complete manifolds with curvature bounds
[article]

2021
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arXiv
*
pre-print

In the second part of the paper, for every n ≥ 2 and p>2 we construct a

arXiv:2011.14630v4
fatcat:doetku4szje75dj3ne7fsoqy5i
*complete*n-dimensional*manifold*with sectional curvature*bounded*from below by a negative constant, for which the density property ... We investigate the density of compactly supported smooth functions in the Sobolev space W^k,p on*complete*Riemannian*manifolds*. ... Let (M, g) be a*complete*Riemannian*manifold*. Define λ as in (2) . ...##
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A lower bound of the integrated Carathéodory–Reiffen metric and Invariant metrics on complete noncompact Kähler manifolds
[article]

2022
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arXiv
*
pre-print

metric with some other moderate conditions on n-dimensional

arXiv:2109.14473v2
fatcat:2azlpjtyhjgrrjrztypojglrea
*complete*noncompact Kähler*manifolds*. ... In this paper, we attempt to make progress on the following long-standing conjecture in hyperbolic complex geometry: a simply connected*complete*Kähler*manifold*(M, ω) with negatively pinched sectional ... Let (M, ω) be an n-dimensional*complete*Kähler*manifold*. ...##
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Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below
[article]

2019
*
arXiv
*
pre-print

Given a smooth positive measure μ on a

arXiv:1804.07540v2
fatcat:yvveadzkhneijlzirzc6df52ei
*complete*Hermitian*manifold*with Ricci curvature*bounded*from below, we prove a pointwise Agmon-type*bound*for the corresponding Bergman kernel, under rather general ... Our results extend several known*bounds*in the literature to the case in which the*manifold*is neither assumed to be Kähler nor of "*bounded*geometry". ... Let (M, h) be a*complete*Kähler*manifold*with Ricci curvature*bounded*from below. ...##
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Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below, III

2012
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Journal of the Mathematical Society of Japan
*

Shiohama on the occasion of his seventieth birthday: This article is the third in a series of our investigation on a

doi:10.2969/jmsj/06410185
fatcat:27xhspwhebgrzogevz6o3ri57m
*complete*non-compact connected Riemannian*manifold*M. ... A von Mangoldt surface of revolution is, by definition, a*complete*surface of revolution homeomorphic to Euclidean plane whose Gaussian curvature is non-increasing along each meridian. ... Main Theorem Let (M, p) be a*complete*non-compact connected Riemannian n-*manifold*M whose radial curvature at the base point p is*bounded*from below by that of a noncompact model surface of revolution ...
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