A. Logunov

activity

20132026

most citedOn ratios of harmonic functions

15 citations · 47 across the 16 of their papers we have counts for

collaborators

Showing 2016Show all

3 papers · 1 filter

math.AP2016★ 4 cited

Nodal sets of Laplace eigenfunctions: estimates of the Hausdorff measure in dimension two and three

Alexander Logunov, Eugenia Malinnikova

Let $Δ_{M}$ be the Laplace operator on a compact $n$ -dimensional Riemannian manifold without boundary. We study the zero sets of its eigenfunctions $u : Δ u + λ u = 0$ . In dimension $n = 2$ …

math.AP2016

Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture

Alexander Logunov

Let $u$ be a harmonic function in the unit ball $B (0, 1) \subset R^{n}$ , $n \geq 3$ , such that $u (0) = 0$ . Nadirashvili conjectured that there exists a positive constant $c$ , d…

math.AP2016

Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure

Alexander Logunov

Let $M$ be a compact $C^{\infty}$ -smooth Riemannian manifold of dimension $n$ , $n \geq 3$ , and let $φ_{λ} : Δ_{M} φ_{λ} + λ φ_{λ} = 0$ denote the Laplace eigenfunction on $M$ co…