Bound sets for a class of ϕ-Laplacian operators

2021 ◽  
Vol 297 ◽  
pp. 508-535
Author(s):  
Guglielmo Feltrin ◽  
Fabio Zanolin
Keyword(s):  
Laplacian Operators ◽  
Bound Sets

scholarly journals Bootstrap bounds on closed Einstein manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James Bonifacio ◽  
Kurt Hinterbichler
Keyword(s):  
Compact Riemannian Manifold ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Consistency Conditions ◽  
Conformal Field ◽  
Geometric Data ◽  
Conformal Bootstrap ◽  
Laplacian Operators ◽  
Kaluza Klein

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

Adaptive regularized noise smoothing of dense range image using directional Laplacian operators

2001 ◽  
Author(s):  
Jeong-Ho Shin ◽  
Yiyong Sun ◽  
Woongchan Jung ◽  
Joon-Ki Paik ◽  
Mongi A. Abidi
Keyword(s):  
Range Image ◽  
Dense Range ◽  
Laplacian Operators ◽  
Noise Smoothing

GAPS IN THE RATIOS OF THE SPECTRA OF LAPLACIANS ON FRACTALS

Fractals ◽  
2009 ◽  
Vol 17 (04) ◽  
pp. 523-535 ◽  
Author(s):  
KATHRYN E. HARE ◽  
DENGLIN ZHOU
Keyword(s):  
Fourier Series ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Classical Setting ◽  
Counting Formula ◽  
Laplacian Operators ◽  
Surprising Fact ◽  
Better Than

In contrast to the classical situation, it is known that many Laplacian operators on fractals have gaps in their spectrum. This surprising fact means there can be no limit in the Weyl counting formula and it is a key ingredient in proving that the convergence of Fourier series on fractals can be better than in the classical setting. Recently, it was observed that the Laplacian on the Sierpinski gasket has the stronger property that there are intervals which contain no ratios of eigenvalues. In this paper we give general criteria for this phenomena and show that Laplacians on many interesting classes of fractals satisfy our criteria.

scholarly journals Bound sets and two-point boundary value problems for second order differential systems

2019 ◽  
Vol 144 (4) ◽  
pp. 373-392
Author(s):  
Jean Mawhin ◽  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Differential Systems ◽  
Bound Sets
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