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Sep 14 at 18:44 comment added Student Thank you very much for this answer! I was curious about this because this showed up in the proof of proposition 2.25 in the Colding-Minicozzi Minimal Surface Book where they essentially prove that if a minimal surface can be approached from one side by a sequence of minimal graphs $|u_j|+|\nabla u_j|\to 0$ then it must be stable. This lemma uses the above estimate, so I was curious whether this holds true in higher dimensions.
Sep 14 at 18:37 history bounty ended Student
Sep 10 at 2:32 vote accept Student
Sep 9 at 22:21 history answered Connor Mooney CC BY-SA 4.0