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.

ON THE LOWER BOUND ESTIMATES OF SECTIONS OF THE CANONICAL BUNDLES OVER A RIEMANN SURFACE

2001 ◽  
Vol 12 (08) ◽  
pp. 891-926 ◽  
Author(s):  
ZHIQIN LU
Keyword(s):  
Riemann Surface ◽  
Lower Bound ◽  
Uniform Estimate ◽  
Gauss Curvature ◽  
Corona Problem ◽  
Lower Bound Estimate

We give a lower bound estimate of the sum of the square norm of the sections of the pluricanonical bundles over a Riemann surface of genus greater than 2 and Gauss curvature -1. Such an estimate must depend on the injective radius of the Riemann surface. However, using this estimate, we give a uniform estimate of the corona problem on Riemann surface. Here "uniform" means that the estimate depends only on the genus of Rieman surface, not on the injective radius.

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

scholarly journals On Lax pairs and matrix extended simple Toda systems

2005 ◽  
Vol 2005 (17) ◽  
pp. 2735-2747
Author(s):  
M. Legaré
Keyword(s):  
Lax Pair ◽  
Lax Pairs ◽  
Toda System ◽  
Toda Systems

AA1Toda system is extended via Lax pair formulations in order to probe noncommutative variables extensions. Systems, some solvable, are built using matrix generalizations.

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

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