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Summer 2016 Viscosity solutions, ends and ideal boundaries
Xiaojun Cui
Illinois J. Math. 60(2): 459-480 (Summer 2016). DOI: 10.1215/ijm/1499760017

Abstract

On a smooth, non-compact, complete, boundaryless, connected Riemannian manifold $(M,g)$, there are three kinds of objects that have been studied extensively:

$\bullet $ Viscosity solutions to the Hamilton–Jacobi equation determined by the Riemannian metric;

$\bullet $ Ends introduced by Freudenthal and more general other remainders from compactification theory;

$\bullet $ Various kinds of ideal boundaries introduced by Gromov.

In this paper, we will present some initial relationship among these three kinds of objects and some related topics are also considered.

Citation

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Xiaojun Cui. "Viscosity solutions, ends and ideal boundaries." Illinois J. Math. 60 (2) 459 - 480, Summer 2016. https://doi.org/10.1215/ijm/1499760017

Information

Received: 16 July 2015; Revised: 26 January 2017; Published: Summer 2016
First available in Project Euclid: 11 July 2017

zbMATH: 1377.49027
MathSciNet: MR3680543
Digital Object Identifier: 10.1215/ijm/1499760017

Subjects:
Primary: 49L25, 53C22, 53D25, 70H20

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 2 • Summer 2016
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