Notes on the differentiation of quasi-convex functions

F. Reese Harvey; H. Blaine Lawson Jr

Notes on the differentiation of quasi-convex functions

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arxiv 1309.1772 v3 pith:W6RMB2CP submitted 2013-09-06 math.AP math.CAmath.CVmath.DG

F. Reese Harvey , H. Blaine Lawson Jr This is my paper · ORCID

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keywords basicfunctionsquasi-convexadequatealongapplycasescombined

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This expository paper presents elementary proofs of four basic results concerning derivatives of quasi-convex functions. They are combined into a fifth theorem which is simple to apply and adequate in many cases. Along the way we establish the equivalence of the basic lemmas of Jensen and Slodkowski.

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Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds
math.DG 2019-08 accept novelty 7.0 of 10

The paper proves in all dimensions that the total curvature inequality implies the isoperimetric inequality in Cartan-Hadamard manifolds, and establishes a new comparison formula for total curvature of level sets.

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