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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제59권 제1호
- 발행연도
- 2022.1
- 수록면
- 13 - 33 (21page)
- DOI
- 10.4134/JKMS.j200626
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초록· 키워드
오류제보하기
The quaternionic Calabi conjecture was introduced by \linebreak Alesker-Verbitsky, analogous to the K\"ahler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a flat hyperK\"ahler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic \MA~equation. Our goal is to prove the long time existence and $C^{\infty}$ convergence for normalized solutions as $t\ri\infty$. As a consequence, we show that the limit function is exactly the solution of quaternionic \MA~equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.
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