Some remarks concerning integrals of curvature on curves and surfaces

Details Some remarks concerning integrals of curvature on curves and surfaces Some remarks concerning integrals of curvature on curves and surfaces

2001-08-29

arxiv.org/abs/math/0108203v3

Mathematics

Classical Analysis and ODEs

Latex-2e, 11 pages. Minor adjustments, and a number of additional references concerning other connections between Cauchy kerne

Scientific paper

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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