Do you mind ______ down the volume a little, please?

Would you mind? and Do you mind?
We use the phrases would you mind + -ing form, and do you mind + -ing form to ask people politely to do things. Would you mind is more polite and more common:
Would you mind opening the window, please?
Do you mind turning down the volume a little, please?
Do you mind me turning on the light? (I want to turn on the light)