Upper bound of Kähler angles on the β-symplectic critical surfaces

Abstract

Let (M,g) be a Kähler surface and \mathrm{\Sigma } be a \beta-symplectic critical surface in M. If L_q\left(\mathrm{\Sigma }\right) is bounded for some q>3, then we give a uniform upper bound for the Kähler angle on \mathrm{\Sigma }. This bound only depends on M,q,\beta and the L_q functional of \mathrm{\Sigma }. For q>4, this estimate is known and we extend the scope of q.

Key words： Kähler surface; β-symplectic critical surfaces; Kähler angle; L_β functional

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11871436).

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