Has anyone ever heard about a Complex Laplace Operator? I would like to build one from first principles as in differential geometry ∆=d*d, where d is the exterior derivative, but I don't know where to start. Actually, I was even unsure in which forum to post the question. If one defines d to be the gradient operator acting on continuous or discrete functions, then one gets the canonical Laplace operator or the Laplace matrix used in graph theory and image processing. But what if one consider complex-valued functions?