On realization of tangent cones of homologically area-minimizing compact singular submanifolds

TL;DR

This paper demonstrates that all area-minimizing hypercones and Lawlor cones can be realized as tangent cones at points of homologically area-minimizing singular compact submanifolds, extending previous results.

Contribution

It shows the realization of specific cones as tangent cones of homologically area-minimizing submanifolds, generalizing prior work by Smale.

Findings

All area-minimizing hypercones are realizable as tangent cones.

Lawlor cones can be realized as tangent cones.

Extension of Smale's result to a broader class of cones.

Abstract

We show that every area-minimizing hypercone and every oriented Lawlor cone in [Law91] can be realized as a tangent cone at a point of some homologically area-minimizing singular compact submanifold. In particular this generalizes the result of N. Smale [Sma99].