me/my两者都可.

从理论上说, me和my都可, 但me 等人称代词宾格来作doing的逻辑主语更常见.

如: Would you mind my opening the window ?
我打开窗子你介意吗?

Would you mind us playing here?
我们在这儿玩,好不好 ?

Would you mind me turning down the music sound?
我把音量关小一点,你不介意吧 ?