A continuous geometric Borg theorem on flat tori
Year: 2026
Type: article
Abstract: Let V ∈ C ∞ ( T d ; R ) V\in C^\infty (\mathbb {T}^d;\mathbb {R}) , d ≥ 2 d\geq 2 , where T d = R d / ( 2 π Z ) d \mathbb {T}^d=\mathbb {R}^d/(2\pi \mathbb {Z})^d , and let \[ H ( k ) = ( − i ∇ + k ) 2 + V ( x ) , k ∈ C d , H(k)=(-i\nabla +k)^2+V(x),\qquad k\in \mathbb {C}^d, \] act on periodic functions on T d \mathbb {T}^d . We prove that the Bloch variety of H H contains the graph of an entire function f : C d → C
DOI: 10.1090/cams/87
Author: Yi Huang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7225614786