4 papers · 1 filter
On filtration formula and nodal sets in min-max theory
Talant Talipov
Let be a closed smooth Riemannian manifold, and let \[ 0=λ_0\leqλ_1\leq\ldots \] be the spectrum of the Laplace-Beltrami operator, with corresponding real eigenfuncti…
Minimal spheres and scalar curvature
Talant Talipov
In 1982, S.-T. Yau conjectured that there exist four distinct embedded minimal two-spheres in any manifold diffeomorphic to . Wang-Zhou confirmed this conjecture for Riemannia…
Equivalence of Almgren-Pitts and phase-transition half-volume spectra
Talant Talipov
We prove that the Almgren-Pitts and phase-transition half-volume spectra of a closed Riemannian manifold are equal. This confirms a conjecture of Liam Mazurowski and Xin Zhou.
Morse index of min-max stationary integral varifolds
Mitchell Gaudet, Talant Talipov
We prove an upper bound for the Morse index of min-max stationary integral varifolds realizing the -dimensional -width of a closed Riemannian manifold.