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Bounded Manifold Completion [article]

Kelum Gajamannage, Randy Paffenroth
2019 arXiv   pre-print
In this paper, we will present a thematically different approach to detect the existence of a low-dimensional 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).  ... 
arXiv:1912.09026v1 fatcat:hr2v7yuxdzednhxj3zkduzxwkq

Complete manifolds with bounded curvature and spectral gaps [article]

Richard Schoen, Hung Tran
2017 arXiv   pre-print
We study the spectrum of 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.  ... 
arXiv:1510.05046v2 fatcat:dxahimnl75c67jx6wnm4rpyl3y

Density of bounded maps in Sobolev spaces into complete manifolds

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen
2017 Annali di Matematica Pura ed Applicata  
Given a 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.  ... 
doi:10.1007/s10231-017-0664-1 fatcat:fccjxrv6yjdj7kbszm45tnz2ji

Bounded harmonic $1$-forms on complete manifolds

M. Cocos
2008 Proceedings of the American Mathematical Society  
In this paper we present some results concerning 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.  ... 
doi:10.1090/s0002-9939-08-09645-7 fatcat:6ygsexsyknecdcoukktvzzlxne

Remark on a diameter bound for complete manifolds with positive Bakry-Émery Ricci curvature [article]

Homare Tadano
2015 arXiv   pre-print
In this paper, we shall give a new upper diameter estimate for 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.  ... 
arXiv:1504.05384v2 fatcat:xxt2bttzcffqvjxud6lpnuzeyu

Extension of holomorphic canonical forms on complete d-bounded Kahler manifolds [article]

Chunle Huang
2020 arXiv   pre-print
In this paper we study the extension of holomorphic canonical forms on 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.  ... 
arXiv:2004.13246v1 fatcat:auyup3ncpjdovivdacpm5wa4q4

TOPOLOGY OF COMPLETE FINSLER MANIFOLDS WITH RADIAL FLAG CURVATURE BOUNDED BELOW

Kei KONDO, Shin-ichi OHTA, Minoru TANAKA
2014 Kyushu Journal of Mathematics  
We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler 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)  ... 
doi:10.2206/kyushujm.68.347 fatcat:r4xd5eehdvd6fhhn7zn4zxkgy4

Complete manifolds with bounded curvature and spectral gaps

Richard Schoen, Hung Tran
2016 Journal of Differential Equations  
We study the spectrum of 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.  ... 
doi:10.1016/j.jde.2016.05.002 fatcat:tjk6gptilnenfkg5k6rkpzr4dm

Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry [article]

Abraham Muñoz Flores, Stefano Nardulli
2016 arXiv   pre-print
, to this class of noncompact 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).  ... 
arXiv:1404.3245v3 fatcat:v74xhiqxkrevnmwdnifsjvji24

Weak approximation by bounded Sobolev maps with values into complete manifolds

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen
2018 Comptes rendus. Mathematique  
We have recently introduced the trimming property for a 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.  ... 
doi:10.1016/j.crma.2018.01.017 fatcat:xlpkghvncrbh3jn3jfj4de5uzm

Poincaré inequality on complete Riemannian manifolds with Ricci curvature bounded below [article]

Gérard Besson, Gilles Courtois, Sa'ar Hersonsky
2018 arXiv   pre-print
We prove that 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).  ... 
arXiv:1801.04216v1 fatcat:3j4p6nxt75ez3gcsueazzl3rre

Density and non-density of C^∞_c ↪ W^k,p on complete manifolds with curvature bounds [article]

Shouhei Honda, Luciano Mari, Michele Rimoldi, Giona Veronelli
2021 arXiv   pre-print
In the second part of the paper, for every n ≥ 2 and p>2 we construct a 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) .  ... 
arXiv:2011.14630v4 fatcat:doetku4szje75dj3ne7fsoqy5i

A lower bound of the integrated Carathéodory–Reiffen metric and Invariant metrics on complete noncompact Kähler manifolds [article]

Gunhee Cho, Kyu-Hwan Lee
2022 arXiv   pre-print
metric with some other moderate conditions on n-dimensional 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.  ... 
arXiv:2109.14473v2 fatcat:2azlpjtyhjgrrjrztypojglrea

Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below [article]

Franz Berger, Gian Maria Dall'Ara, Duong Ngoc Son
2019 arXiv   pre-print
Given a smooth positive measure μ on a 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.  ... 
arXiv:1804.07540v2 fatcat:yvveadzkhneijlzirzc6df52ei

Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below, III

Kei KONDO, Minoru TANAKA
2012 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 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  ... 
doi:10.2969/jmsj/06410185 fatcat:27xhspwhebgrzogevz6o3ri57m
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