Surfaces of prescribed Gauss curvature
The basic problem is to understand under what conditions it is possible to find a convex surface of prescribed Gauss curvature which also satisfies some boundary conditions.
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The basic problem is to understand under what conditions it is possible to find a convex surface of prescribed Gauss curvature which also satisfies some boundary conditions. It is also interesting to look at these questions for curvatures other than the mean and Gauss curvatures, but this is more diffcult and less well understood.
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Emeritus Professor