Successive Minima-Type Inequalities
summary
Defines and works with successive minima and proves volume and counting analogues: classical bounds like volume≥2^n ⇒ nontrivial lattice point and Minkowski's second theorem (upper bound ~2^n, lower ~1/n!) are reviewed. Generalizations use the symmetral K_C; the Ehrhard conjecture (centroid at origin, threshold ~e^n) remains open. Introduces packing minima ρ_i from lattice projections and gets a discrete bound on lattice points, roughly #K∩Z^n ≤ ∏(2/ρ_i(K)+1), with known dimension-dependent factor losses in higher n.
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