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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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Poincaré-Hopf Theorem for domains with a point of vanishing curvature

Consider $\Omega \subset \mathbb{R}^2$ a convex planar domain having positive curvature on the boundary except for a point $p \in \partial \Omega$ where the curvature vanishes. I would like to know wh …