Geodesic
Geometric versions of Schwarz’s lemma for spherically convex functions
Canadian journal of mathematics, Tome 75 (2023) no. 6, pp. 1780-1799

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DOI

We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area, and total spherical curvature. These results can be viewed as geometric variants of the classical Schwarz lemma for spherically convex functions.
DOI : 10.4153/S0008414X22000529
Mots-clés : Spherical metric, spherical convexity, spherical length, spherical area, Gauss–Bonnet formula, isoperimetric inequality, spherical curvature 
Kourou, Maria; Roth, Oliver. Geometric versions of Schwarz’s lemma for spherically convex functions. Canadian journal of mathematics, Tome 75 (2023) no. 6, pp. 1780-1799. doi: 10.4153/S0008414X22000529
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     title = {Geometric versions of {Schwarz{\textquoteright}s} lemma for spherically convex functions},
     journal = {Canadian journal of mathematics},
     pages = {1780--1799},
     year = {2023},
     volume = {75},
     number = {6},
     doi = {10.4153/S0008414X22000529},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000529/}
}
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