Elisabetta Barletta

Yang–Mills fields on CR manifolds

We study pseudo Yang–Mills fields on a compact strictly pseudoconvex CR manifold M, i.e., the critical points of the functional PYM(D)=12∫M∥πHRD∥2θ∧(dθ)n, where D is a connection in a Hermitian CR holomorphic vector bundle (E,h)→M. Let Ω={φ<0}⊂Cn be a smoothly bounded strictly pseuodoconvex domain and g the Bergman metric on Ω. We show that boundary values Db of Yang–Mills fields D on (Ω,g) are pseudo Yang–Mills fields on ∂Ω, provided that iTRDb=0 and iNRD=0 on H(∂Ω). If S1→C(M)→πM is the canonical circle bundle and π*D is a Yang–Mills field with respect to the Fefferman metric Fθ of (M,θ) then D is a pseudo Yang–Mills field on M. The Yang–Mills equations δπ*DRπ*D=0 project on the Euler–Lagrange equations δbDRD=0 of the variational principle δPYM(D)=0, provided that iTRD=0. When M has vanishing pseudohermitian Ricci curvature the pullback π*D of the (CR invariant) Tanaka connection D of (E,h) is a Yang–Mills field on C(M). We derive the second variation formula {d2PYM(Dt)∕dt2}t=0=∫M⟨SbD(φ),φ⟩θ∧(dθ)n, Dt=D...

On Transversally Holomorphic Maps of Kählerian Foliations

AbstractAny transversally holomorphic foliated map

Combinatorial PDEs on Hamming graphs

\varphi :(M,\mathcal{F}) \to (M\prime ,\mathcal{F}\prime )

On Lewy's unsolvability phenomenon

of Kählerianfoliations with

A New Upper Bound on the Cheeger Number of a Graph

\mathcal{F}

CR Submanifolds of Hermitian Manifolds and the Tangential CR Equations

harmonic, is shown to be a transversallyharmonic map and an absolute minimum of the energy functional