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Isoperimetric inequalities for immersed closed spherical curves

Isoperimetric inequalities for immersed closed spherical curves

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha colon upper S Superscript 1 Baseline right-arrow upper S squared"> <mml:semantics> <mml:mrow> <mml:mi>α<!-- α --></mml:mi> <mml:mo>:</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:mo stretchy="false">→<!-- → --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\alpha :{S^1} \to {S^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be …