Interpolation of generalized Heegner cycles in Coleman families

Kobayashi recently proved that the generalized Heegner cycles of Bertolini–Darmon–Prasanna can be interpolated along the anticyclotomic tower, giving rise to distribution valued cohomology classes with expected growth rate. We interpolate these classes along Coleman families. This construction plays a role in the proofs of p-adic Gross–Zagier formulae at for non-ordinary eigenforms and consequentially, also in the proof of a conjecture of Perrin-Riou.