The p-widths of a surface
نویسندگان
چکیده
Abstract The $p$ p -widths of a closed Riemannian manifold are nonlinear analogue the spectrum its Laplace–Beltrami operator, which corresponds to areas certain min-max sequence possibly singular minimal submanifolds. We show that any two-manifold correspond union immersed geodesics, rather than simply geodesic nets. then prove optimality sweepouts round two-sphere constructed from zero set homogeneous polynomials, showing sphere attained by $\lfloor \sqrt{p}\rfloor $ ⌊ ⌋ great circles. As result, we find universal constant in Liokumovich–Marques–Neves–Weyl law for surfaces be $\sqrt{\pi }$ π . En route calculating two-sphere, two additional new results: bumpy metrics theorem stationary nets with fixed edge lengths, and that, generically, bounded mass have Lusternik–Schnirelmann category zero.
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ژورنال
عنوان ژورنال: Publications Mathématiques de l'IHÉS
سال: 2023
ISSN: ['0073-8301', '1618-1913']
DOI: https://doi.org/10.1007/s10240-023-00141-7