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This page hosts a collection of expository notes and drafts on topics or problems I find interesting.drafts
- A Curvature Criterion for Monotonicity of Domains
We extend a definition of monotonicity given for polygons to higher dimensional domains and establish a criterion which implies that a given domain is monotone with respect to at least one direction in terms of an inequality involving the total absolute Gauss-Kronecker curvature of its boundary. As a corollary of this result, we show that all polygons with five or fewer sides are monotone.