Uniform pointwise asymptotic estimates for positive Jacobi fields

Establish uniform pointwise asymptotic estimates on the entire minimizing leaf for the positive Jacobi field associated with a general area-minimizing hypercone.

Background

The initial PDE-based approach sought to construct the required tangent vector fields by controlling the divergence of a projection field on a foliation leaf. That approach appeared to require uniform pointwise asymptotic estimates for the positive Jacobi field throughout the whole leaf. The paper explicitly states that these estimates could not be established for general minimizing hypercones; the final proof instead avoids this unresolved technical issue by integrating projection kernels with the Jacobi field as a weight.