Rafael López

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math.DG2026

Separable surfaces that are critical points of the Dirichlet energy

Rafael LÃ³pez

In this paper, we study surfaces $z = I ¨ (x, y)$ in Euclidean space that satisfy the equation $I ¨ _{xx} + I ¨ _{y y} = \frac{I ^}{} 2$ where $Î\in\r$ is a real constant. We classify these surface…

math.DG2026

Geometric aspects of the curve shortening flow in the hyperbolic plane

Ivan KrznariÄ, Rafael LÃ³pez

We define a new notion of translations in the hyperbolic plane and explicitly solve the equation of the curve shortening flow. Next, we consider the class of ancient convex solutio…