scholarly journals On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach–Finsler manifolds

2011 ◽  
Vol 74 (11) ◽  
pp. 3487-3500 ◽  
Author(s):  
M. Jiménez-Sevilla ◽  
L. Sánchez-González
Keyword(s):  
Lipschitz Functions ◽  
Smooth Approximation ◽  
Finsler Manifolds ◽  
Smooth Extension

scholarly journals Smooth Approximation of Lipschitz Functions on Finsler Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. I. Garrido ◽  
J. A. Jaramillo ◽  
Y. C. Rangel
Keyword(s):  
Lipschitz Function ◽  
Composition Operators ◽  
Lipschitz Functions ◽  
Finsler Manifold ◽  
Positive Continuous Function ◽  
Smooth Approximation ◽  
Finsler Manifolds ◽  
Lipschitz Constants ◽  
Bounded Derivative

We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz functionf:M→ℝdefined on a connected, second countable Finsler manifoldM, for each positive continuous functionε:M→(0,∞)and eachr>0, there exists aC1-smooth Lipschitz functiong:M→ℝsuch that|f(x)-g(x)|≤ε(x), for everyx∈M, andLip(g)≤Lip(f)+r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebraCb1(M)of allC1functions with bounded derivative on a complete quasi-reversible Finsler manifoldM, we obtain a characterization of algebra isomorphismsT:Cb1(N)→Cb1(M)as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.

scholarly journals Smooth approximation of Lipschitz functions on Riemannian manifolds

2007 ◽  
Vol 326 (2) ◽  
pp. 1370-1378 ◽  
Author(s):  
D. Azagra ◽  
J. Ferrera ◽  
F. López-Mesas ◽  
Y. Rangel
Keyword(s):  
Riemannian Manifolds ◽  
Lipschitz Functions ◽  
Smooth Approximation

Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group

2013 ◽  
Vol 49 (3-4) ◽  
pp. 1279-1308 ◽  
Author(s):  
Giovanna Citti ◽  
Maria Manfredini ◽  
Andrea Pinamonti ◽  
Francesco Serra Cassano
Keyword(s):  
Heisenberg Group ◽  
Lipschitz Functions ◽  
Smooth Approximation

Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds

2020 ◽  
Vol 279 (8) ◽  
pp. 108662
Author(s):  
Aris Daniilidis ◽  
Jesus A. Jaramillo ◽  
Francisco Venegas M.
Keyword(s):  
Lipschitz Functions ◽  
Finsler Manifolds

scholarly journals Sufficient Criteria for Obtaining Hardy Inequalities on Finsler Manifolds

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Ágnes Mester ◽  
Ioan Radu Peter ◽  
Csaba Varga
Keyword(s):  
Finsler Manifolds ◽  
Hardy Inequalities
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