Acta Mathematica

Volume 221 (2018)

Number 1

On the structure of band edges of $2$-dimensional periodic elliptic operators

Pages: 59 – 80



Nikolay Filonov (V. A. Steklov Mathematical Institute, St. Petersburg, Russia; and St. Petersburg State University, St. Petersburg, Russia)

Ilya Kachkovskiy (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)


For a wide class of $2$-dimensional periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated.


periodic Schrödinger operator, Bloch eigenvalues, spectral band edges, effective mass

To the memory of Yuri Safarov, our dear friend and colleague

The first author was supported by RFBR Grant 16–01–00087 and by Simons Foundation. The second author was supported by AMS Simons Travel Grant 2014–2016 and by NSF grant DMS–1758326.

Received 26 March 2016

Accepted 29 June 2018

Published 6 November 2018