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The least area bounded by multiples of a curve

The least area bounded by multiples of a curve

For each positive integer <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we construct a smooth curve <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma"> <mml:semantics> <mml:mi mathvariant="normal">Γ<!-- Γ --></mml:mi> <mml:annotation encoding="application/x-tex">\Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper R Superscript 4"> <mml:semantics> <mml:mrow …