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OPTIMALLY IMMERSED PLANAR CURVES UNDER MÖBIUS ENERGY

RYAN P. DUNNING

St. Mary's University, One Camino Santa Maria, San Antonio, TX 78228-8560, USA

https://doi.org/10.1142/S0218216511009509Cited by:1 (Source: Crossref)

Abstract

This paper investigates the existence of optimally immersed planar self-intersecting curves. Because any self-intersecting curve will have infinite knot energy, parameter-dependent renormalizations of the Möbius energy remove the singular behavior of the curve. The direct method of the calculus of variations allows for the selection of optimal immersions in various restricted classes of curves. Careful energy estimates allow subconvergence of these optimal curves as restrictions are relaxed.

Keywords:

AMSC: 49Q10, 49K30

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