For a wide class of $2$-dimensional periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated.
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.
To the memory of Yuri Safarov, our dear friend and colleague
"On the structure of band edges of $2$-dimensional periodic elliptic operators." Acta Math. 221 (1) 59 - 80, September 2018. https://doi.org/10.4310/ACTA.2018.v221.n1.a2