TY - JOUR
T1 - A COMPACTNESS THEOREM FOR HYPERKÄHLER 4-MANIFOLDS WITH BOUNDARY
AU - Liu, Hongyi
N1 - Publisher Copyright:
© 2024 Duke University Press. All rights reserved.
PY - 2024/4/15
Y1 - 2024/4/15
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.
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U2 - 10.1215/00127094-2023-0037
DO - 10.1215/00127094-2023-0037
M3 - Article
AN - SCOPUS:85194948907
SN - 0012-7094
VL - 173
SP - 1177
EP - 1225
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 6
ER -