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Some remarks concerning integrals of curvature on curves and surfaces

Stephen Semmes
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Abstract

In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using quarternions or Clifford algebras. These topics came up in "Analysis of and on Uniformly Rectifiable Sets" (with Guy David, American Mathematical Society, 1993), and here we describe some of the basic points involved. A presentation based on this paper was made at the AMS Special Session "Surface Geometry and Shape Perception" (Hoboken, 2001).

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Stephen Semmes. 2002-11-19. Some remarks concerning integrals of curvature on curves and surfaces. https://arxiv.org/abs/math/0108203

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