Constant mean curvature discs with bounded area
Constant mean curvature discs with bounded area
It has been long conjectured that the two spherical caps are then only discs in the Euclidean three-space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R cubed"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathbb {R}^3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with non-zero constant mean curvature spanning …