A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
Keyword(s):
Abstract We conjecture that the Gauss–Bonnet formula gives a necessary and sufficient condition for the existence of a metric deformation to obtain a positive/negative Gaussian curvature on a disk. The conjecture is reduced to a problem of a partial differential inequality with Dirichlet–Neumann boundary condition. We give a partial answer and an example.
2005 ◽
Vol 2005
(11)
◽
pp. 1809-1818
◽
1989 ◽
Vol 39
(2)
◽
pp. 161-165
2015 ◽
Vol 26
(1)
◽
pp. 630-644
◽
2017 ◽
Vol E100.A
(12)
◽
pp. 2764-2775
◽
Keyword(s):