Title of article :
The affine Cauchy problem
Author/Authors :
Aledo، نويسنده , , Juan A. and Martيnez، نويسنده , , Antonio and Milلn، نويسنده , , Francisco، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2009
Pages :
14
From page :
70
To page :
83
Abstract :
The aim of this paper is to solve the Cauchy problem for locally strongly convex surfaces which are extremal for the equiaffine area functional. These surfaces are called affine maximal surfaces and here, we give a new complex representation which let us describe the solution to the corresponding Cauchy problem. As applications, we obtain a generalized symmetry principle, characterize when a curve in R 3 can be a geodesic or pre-geodesic of a such surface and study the helicoidal affine maximal surfaces. Finally, we investigate the existence and uniqueness of affine maximal surfaces with a given analytic curve in its singular set.
Keywords :
Affine area , Maximal surfaces , singularities , Cauchy problem , Helicoidal affine maximal surfaces
Journal title :
Journal of Mathematical Analysis and Applications
Serial Year :
2009
Journal title :
Journal of Mathematical Analysis and Applications
Record number :
1559596
Link To Document :
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