scholarly journals The Monge Problem for Distance Cost in Geodesic Spaces

2013 ◽  
Vol 318 (3) ◽  
pp. 615-673 ◽  
Author(s):  
Stefano Bianchini ◽  
Fabio Cavalletti
Keyword(s):  
Monge Problem ◽  
Geodesic Spaces

scholarly journals Some Continuation results in Uniquely Geodesic Spaces

2021 ◽  
Vol 1850 (1) ◽  
pp. 012046
Author(s):  
V.V. Sreya ◽  
P. Shaini
Keyword(s):  
Geodesic Spaces

scholarly journals Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 787-798 ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Diameter Growth ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Finite Generation ◽  
Alexandrov Spaces ◽  
Geodesic Spaces ◽  
Special Case ◽  
Linear Diameter

AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

scholarly journals Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces

2019 ◽  
Vol 39 (1) ◽  
pp. 157-183
Author(s):  
Qing Liu ◽  
◽  
Atsushi Nakayasu ◽  
Keyword(s):  
Geodesic Spaces ◽  
Jacobi Equations

More General Surplus

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
General Result ◽  
Convex Analysis ◽  
Scalar Product ◽  
Sufficient Conditions ◽  
General Function ◽  
Existence Of A Solution ◽  
Generalize Convex ◽  
Monge Problem ◽  
Natural Way

This chapter considers a case with a more general surplus function. It shows that when the scalar-product surplus is replaced by a more general function, much of the machinery put in place in Chapter 6 goes through. In particular, it is possible to generalize convex analysis in a natural way, and to obtain generalized notions of convex conjugates, of convexity, and of a subdifferential that are perfectly suited to the problem. A general result on the existence of dual minimizers is given, as well as sufficient conditions for the existence of a solution to the Monge problem.

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