A COMPACTNESS THEOREM FOR HYPERKÄHLER 4-MANIFOLDS WITH BOUNDARY

Hongyi Liu

doi:10.1215/00127094-2023-0037

A COMPACTNESS THEOREM FOR HYPERKÄHLER 4-MANIFOLDS WITH BOUNDARY

Hongyi Liu

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we study the compactness of a boundary value problem for hyperkähler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkähler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.

Original language	English (US)
Pages (from-to)	1177-1225
Number of pages	49
Journal	Duke Mathematical Journal
Volume	173
Issue number	6
DOIs	https://doi.org/10.1215/00127094-2023-0037
State	Published - Apr 15 2024

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2023-0037

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abstract = "In this paper, we study the compactness of a boundary value problem for hyperk{\"a}hler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperk{\"a}hler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.",

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N2 - In this paper, we study the compactness of a boundary value problem for hyperkähler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkähler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.

AB - In this paper, we study the compactness of a boundary value problem for hyperkähler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkähler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.

UR - https://www.scopus.com/pages/publications/85194948907

UR - https://www.scopus.com/pages/publications/85194948907#tab=citedBy

U2 - 10.1215/00127094-2023-0037

DO - 10.1215/00127094-2023-0037

M3 - Article

AN - SCOPUS:85194948907

SN - 0012-7094

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SP - 1177

EP - 1225

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 6

ER -

A COMPACTNESS THEOREM FOR HYPERKÄHLER 4-MANIFOLDS WITH BOUNDARY

Abstract

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