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Ben McKay
Ben McKay
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If a Caccioppoli set A$A$ is of minimal perimeter in every set K compact set $K$ contained in ansome open set  , can we say Athat $A$ is of minimal perimeter in the open set? If not, please construct a counterexample. This problems arises when I read lemma 9.1 in the book of Guisti  ,minimal surfaces and functions of bounded variation Minimal Surfaces and Functions of Bounded Variation. The author explains "caccioppoliCaccioppoli sets of least area "in such ain this way,sometimes and sometimes he uses "caccioppoli sets of least perimeter".I am confusedthe term Caccioppoli sets of least perimeter.

 

If a Caccioppoli set A is of minimal perimeter in every set K compact contained in an open set  , can we say A is of minimal perimeter in the open set? If not, please construct a counterexample. This problems arises when I read lemma 9.1 in the book of Guisti  ,minimal surfaces and functions of bounded variation. The author explains "caccioppoli sets of least area "in such a way,sometimes he uses "caccioppoli sets of least perimeter".I am confused.

 

If a Caccioppoli set $A$ is of minimal perimeter in every compact set $K$ contained in some open set, can we say that $A$ is of minimal perimeter in the open set? If not, please construct a counterexample. This problems arises when I read lemma 9.1 in the book of Guisti, Minimal Surfaces and Functions of Bounded Variation. The author explains Caccioppoli sets of least area in this way, and sometimes he uses the term Caccioppoli sets of least perimeter.

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user128943
user128943
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about the compactness of minimal surfaces

If a Caccioppoli set A is of minimal perimeter in every set K compact contained in an open set , can we say A is of minimal perimeter in the open set? If not, please construct a counterexample. This problems arises when I read lemma 9.1 in the book of Guisti ,minimal surfaces and functions of bounded variation. The author explains "caccioppoli sets of least area "in such a way,sometimes he uses "caccioppoli sets of least perimeter".I am confused.