scholarly journals Critical Points, the Gauss Curvature Equation and Blaschke Products

2013 ◽  
pp. 133-157 ◽  
Author(s):  
Daniela Kraus ◽  
Oliver Roth
Keyword(s):  
Critical Points ◽  
Gauss Curvature ◽  
Blaschke Products ◽  
Curvature Equation

scholarly journals Vanishing Estimates for Fully Bubbling Solutions of SU (n + 1) Toda Systems at a Singular Source

2018 ◽  
Vol 2020 (18) ◽  
pp. 5774-5795
Author(s):  
Lei Zhang
Keyword(s):  
Riemann Surface ◽  
Gauss Curvature ◽  
Toda System ◽  
Curvature Equation ◽  
Singular Source ◽  
Toda Systems

AbstractFor Gauss curvature equation (or more general Toda systems) defined on 2D spaces, the vanishing rate of certain curvature functions on blowup points is a key estimate for numerous applications. However, if these equations have singular sources, very few vanishing estimates can be found. In this article we consider a Toda system with singular sources defined on a Riemann surface and we prove a very surprising vanishing estimates and a reflection phenomenon for certain functions involving the Gauss curvature.

scholarly journals Conformal scalar curvature equation on Sn: Functions with two close critical points (Twin Pseudo-Peaks)

2018 ◽  
Vol 20 (05) ◽  
pp. 1750051
Author(s):  
Man Chun Leung ◽  
Feng Zhou
Keyword(s):  
Scalar Curvature ◽  
Critical Points ◽  
Reduction Method ◽  
Existence Results ◽  
The Other ◽  
Curvature Equation ◽  
Two Bubbles

By using the Lyapunov–Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on [Formula: see text] ([Formula: see text]) when the prescribed function (after being projected to [Formula: see text]) has two close critical points, which have the same value (positive), equal “flatness” (“twin”; flatness [Formula: see text]), and exhibit maximal behavior in certain directions (“pseudo-peaks”). The proof relies on a balance between the two main contributions to the reduced functional — one from the critical points and the other from the interaction of the two bubbles.

scholarly journals Optimal transport and the Gauss curvature equation

2020 ◽  
Vol 27 (4) ◽  
pp. 387-404
Author(s):  
Nestor Guillen ◽  
Jun Kitagawa
Keyword(s):  
Optimal Transport ◽  
Gauss Curvature ◽  
Curvature Equation
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