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Nov 27 at 22:41 comment added Piotr Hajlasz That is correct. It may have boundary and it the ball is large it may be complicated with a lot of self intersections.
Nov 26 at 21:53 comment added Gonzalo A. Benavides Sorry, I may be misunderstanding your question. In the references I provided they proved the result but for the integrals in the whole domain $M$, which is $C^2$ and without boundary. You would like a similar estimate now for balls within $M$, that of course may have a boundary; am I correct?
Nov 25 at 19:14 comment added Piotr Hajlasz I am sorry, but your answer has very little to do with my question. The problem is that in my question you don't have any regularity of the ball has a large radius.
S Nov 25 at 13:06 review First answers
Nov 25 at 13:42
S Nov 25 at 13:06 history edited LSpice CC BY-SA 4.0
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S Nov 25 at 6:29 review First answers
Nov 25 at 7:13
S Nov 25 at 6:29 history answered Gonzalo A. Benavides CC BY-SA 4.0