scholarly journals On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature

2008 ◽  
Vol 345 (2) ◽  
pp. 628-631 ◽  
Author(s):  
Daniela Kraus ◽  
Oliver Roth
Keyword(s):  
Gaussian Curvature ◽  
Nonnegative Curvature ◽  
Isolated Singularities ◽  
Curvature Equation

scholarly journals The behaviour of solutions of the Gaussian curvature equation near an isolated boundary point

2008 ◽  
Vol 145 (3) ◽  
pp. 643-667 ◽  
Author(s):  
DANIELA KRAUS ◽  
OLIVER ROTH
Keyword(s):  
Continuous Function ◽  
Liouville Equation ◽  
Gaussian Curvature ◽  
Boundary Point ◽  
Classical Result ◽  
Riemannian Metrics ◽  
Higher Order ◽  
Isolated Singularities ◽  
Hölder Continuous ◽  
Curvature Equation

AbstractA classical result of Nitsche [22] about the behaviour of the solutions to the Liouville equation Δu= 4e2unear isolated singularities is generalized to solutions of the Gaussian curvature equation Δu= −κ(z)e2uwhere κ is a negative Hölder continuous function. As an application a higher–order version of the Yau–Ahlfors–Schwarz lemma for complete conformal Riemannian metrics is obtained.

Boundary trace of the solutions of the prescribed Gaussian curvature equation

2000 ◽  
Vol 130 (3) ◽  
pp. 527-560 ◽  
Author(s):  
Michele Grillot ◽  
Laurent Véron
Keyword(s):  
Gaussian Curvature ◽  
Radon Measure ◽  
Borel Measure ◽  
Sufficient Conditions ◽  
Open Ball ◽  
Curvature Equation ◽  
Borel Measures ◽  
Boundary Trace ◽  
Regular Borel Measure ◽  
Prescribed Gaussian Curvature

We study the existence of a boundary trace for minorized solutions of the equation Δu + K (x) e2u = 0 in the unit open ball B2 of R2. We prove that this trace is an outer regular Borel measure on ∂B2, not necessarily a Radon measure. We give sufficient conditions on Borel measures on ∂B2 so that they are the boundary trace of a solution of the above equation. We also give boundary removability results in terms of generalized Bessel capacities.

On the structure of the conformal Gaussian curvature equation on R2. II

1991 ◽  
Vol 290 (1) ◽  
pp. 671-680 ◽  
Author(s):  
Kuo-Shung Cheng ◽  
Wei-Ming Ni
Keyword(s):  
Gaussian Curvature ◽  
Curvature Equation

scholarly journals On gaussian curvature equation in $ \mathbb{R}^2 $ with prescribed nonpositive curvature

2020 ◽  
Vol 40 (6) ◽  
pp. 3201-3214
Author(s):  
Huyuan Chen ◽  
◽  
Dong Ye ◽  
Feng Zhou ◽  
◽  
...  
Keyword(s):  
Gaussian Curvature ◽  
Nonpositive Curvature ◽  
Curvature Equation

scholarly journals On the Conformal Gaussian Curvature Equation inR2

1998 ◽  
Vol 146 (1) ◽  
pp. 226-250 ◽  
Author(s):  
Kuo-Shung Cheng ◽  
Chang-Shou Lin
Keyword(s):  
Gaussian Curvature ◽  
Curvature Equation
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