Talant Talipov

activity

20222026

collaborators

7 papers

math.DG2026

On filtration formula and nodal sets in min-max theory

Talant Talipov

Let $(M^{n + 1}, g)$ 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…

math.DG2026

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 $S^{3}$ . Wang-Zhou confirmed this conjecture for Riemannia…

math.DG2026

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.

math.DG2026

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 $d$ -dimensional $p$ -width of a closed Riemannian manifold.

math.DG2025

Generic density of stationary geodesic nets that are not closed geodesics

Talant Talipov

We prove that for a Baire-generic Riemannian metric on a closed smooth manifold of dimension greater than or equal 3, the union of stationary geodesic nets that are not closed geod…

math.DG2024

Besicovitch-type inequality for closed geodesics on 2-dimensional spheres

Talant Talipov

We prove the existence of a constant $C > 0$ such that for any Riemannian metric $g$ on a 2-dimensional sphere $S^{2}$ , there exist two distinct closed geodesics with lengths $L_{1}$ …

math.MG2022

Gromov-Hausdorff distance between vertex sets of regular polygons inscribed in a given circle

Talant Talipov

We calculate the Gromov-Hausdorff distance between vertex sets of regular polygons endowed with the round metric. We give a full answer for the case of n- and m-gons with m divisib…