Abstract
Let D0 = {x ∈ R n , H0(x) ≤ 1} be a strictly convex domain in R n with n ≤ 3 and Du = {x ∈ R n , Hu(x) ≤ 1}, u ∈ [η, η] be a continuous one-parameter deformation of D0 with lattice-point counting function Nu(T ) := {m ∈ Z n : Hu(m) ≤ T 2 }. The main result of this paper is an estimate for large values of T of the variation of the counting function, Nu(T ), over generic volumepreserving deformations Du.
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