arXiv Open Access 2019

On the existence of minimal Heegaard surfaces

Daniel Ketover Yevgeny Liokumovich Antoine Song

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Abstrak

Let $H$ be a strongly irreducible Heegaard surface in a closed oriented Riemannian $3$-manifold. We prove that $H$ is either isotopic to a minimal surface of index at most one or isotopic to the boundary of a tubular neighborhood about a non-orientable minimal surface with a vertical handle attached. This confirms a long-standing conjecture of J. Pitts and J.H. Rubinstein.

Topik & Kata Kunci

math.DG math.GT

Penulis (3)

Daniel Ketover

Yevgeny Liokumovich

Antoine Song

Format Sitasi

APA MLA BibTeX

Ketover, D., Liokumovich, Y., Song, A. (2019). On the existence of minimal Heegaard surfaces. https://arxiv.org/abs/1911.07161

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓