التفاصيل البيبلوغرافية
| العنوان: |
Rigidity and vanishing theorems for submanifolds with free boundary in the unit ball. |
| المؤلفون: |
Zhao, Entao, Cao, Shunjuan |
| المصدر: |
Bulletin of the London Mathematical Society; May2024, Vol. 56 Issue 5, p1819-1838, 20p |
| مصطلحات موضوعية: |
UNIT ball (Mathematics), VANISHING theorems, GEOMETRIC rigidity, SUBMANIFOLDS, FREE groups, CURVATURE |
| مستخلص: |
In this paper, we investigate the rigidity and vanishing properties of compact submanifolds with free boundary of arbitrary codimension in the unit ball. We first show that a minimal submanifold with free boundary in the unit ball satisfying a pointwise or integral curvature pinching condition on the second fundamental form is a flat equatorial disk. Then we prove a vanishing theorem for cohomology groups for submanifolds with free boundary in the unit ball under an integral curvature pinching condition on the trace‐free second fundamental form. [ABSTRACT FROM AUTHOR] |
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