English

Minimal submanifolds with multiple isolated singularities

Differential Geometry 2025-03-10 v4 Analysis of PDEs

Abstract

We extend Smale's singular bridge principle [Ann. of Math. 130 (1989), 603-642] for nn-dimensional strictly stable minimal cones in Rn+1\mathbb{R}^{n+1} (n7(n \geq 7) to arbitrary codimension and each n3n \geq 3. We then apply the procedure to copies of the Lawson-Osserman cone to produce a four dimensional minimal graph in R7\mathbb{R}^7 with any finite number of isolated singularities.

Keywords

Cite

@article{arxiv.2409.20327,
  title  = {Minimal submanifolds with multiple isolated singularities},
  author = {Bryan Dimler},
  journal= {arXiv preprint arXiv:2409.20327},
  year   = {2025}
}

Comments

55 pages. Revised: This version completes the generalization of Smale's singular bridge principle to high codimension. The bridge constructions and many proofs have been simplified, and the introduction and closing remarks have been expanded. Comments welcome!

R2 v1 2026-06-28T19:02:22.567Z