7 citations · 12 across the 4 of their papers we have counts for
9 papers
The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions
A. Logunov, E. Malinnikova, N. Nadirashvili +1
Let be a bounded domain in with boundary and let be a Dirichlet Laplace eigenfunction in with eigenvalue . We show that the -dimensio…
An elliptic adaptation of ideas of Carleman and Domar from complex analysis related to Levinson's log log theorem
Alexander Logunov, Hristo Papazov
Using the three balls inequality, we adapt the elegant ideas of Carleman and Domar from complex analysis to linear elliptic PDE and generalize the classical Levinson's loglog theor…
Review of Yau's conjecture on zero sets of Laplace eigenfunctions
Alexander Logunov, Eugenia Malinnikova
This is a review of old and new results and methods related to the Yau conjecture on the zero set of Laplace eigenfunctions. The review accompanies two lectures given at the confer…
Lecture notes on quantitative unique continuation for solutions of second order elliptic equations
Alexander Logunov, Eugenia Malinnikova
In these lectures we present some useful techniques to study quantitative properties of solutions of elliptic PDEs. Our aim is to outline a proof of a recent result on propagation…
Eigenfunctions with infinitely many isolated critical points
Lev Buhovsky, Alexander Logunov, Mikhail Sodin
We construct a Riemannian metric on the -dimensional torus, such that for infinitely many eigenvalues of the Laplace-Beltrami operator, a corresponding eigenfunction has infin…
Collapsing Superstring Conjecture
Alexander Golovnev, Alexander S. Kulikov, Alexander Logunov +2
In the Shortest Common Superstring (SCS) problem, one is given a collection of strings, and needs to find a shortest string containing each of them as a substring. SCS admits $2\fr…