12 papers
Local and non-local -energies on metric measure spaces
Meng Yang
For , we study subordination phenomena for local and non-local regular -energies on metric measure spaces. Under suitable geometric assumptions, we show that if a local reg…
A Gutzwiller trace formula for singular potentials
Jared Wunsch, Mengxuan Yang, Yuzhou Joey Zou
The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectori…
Logarithmic wave decay for short range wavespeed perturbations with radial regularity
Gayana Jayasinghe, Katrina Morgan, Jacob Shapiro +1
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbatio…
On the dichotomy of -walk dimensions on metric measure spaces
Meng Yang
On a volume doubling metric measure space endowed with a family of -energies such that the Poincaré inequality and the cutoff Sobolev inequality with -walk dimension ho…
Flat bands, Dirac cones, and higher-order band crossings in twisted multilayer graphene
Bryan Li, Mengxuan Yang
For the chiral limit of two sheets of -layer Bernal-stacked graphene established in the Physical Review Letters arXiv:2109.10325 and arXiv:2109.11514, we prove a trichotomy: dep…
Energy inequalities for cutoff functions of -energies on metric measure spaces
Meng Yang
For , and for a -energy on a volume doubling metric measure space, we provide several geometric and functional conditions for the validity of the cutoff Sobolev inequality.…
Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
Fabrice Baudoin, Li Chen, Meng Yang
We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform vo…
Wannier decay and the Thouless conjecture
Simon Becker, Zhongkai Tao, Mengxuan Yang
Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch…
On singularity of -energy measures on metric measure spaces
Meng Yang
For , we prove that, for a -energy on a volume doubling metric measure space, the Poincaré inequality and the cutoff Sobolev inequality, both with -walk dimension strict…
A direct proof of the cutoff Sobolev inequality on the Sierpiński gasket
Meng Yang
We present a direct proof of the cutoff Sobolev inequality on the Sierpiński gasket, which has long been regarded as highly non-trivial in the context of heat kernel estimates.
-Poincaré inequalities and cutoff Sobolev inequalities on metric measure spaces
Meng Yang
For , we introduce the cutoff Sobolev inequality on general metric measure spaces, and prove that there exists a metric measure space endowed with a -energy that satisfies…
Hölder regularity of harmonic functions on metric measure spaces
Jin Gao, Meng Yang
We introduce a Hölder regularity condition for harmonic functions on metric measure spaces and prove that, under a slow volume regular condition and an upper heat kernel estimate,…