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SNSMathPreprintServer-http://math.sns.it/papers/emiman03/CVGMTPreprintServer-http://cvgmt.sns.it/papers/emiman03/ SOME PROPERTIES OF THE DISTANCE FUNCTION AND A
 

Summary: SNSMathPreprintServer-http://math.sns.it/papers/emiman03/CVGMTPreprintServer-http://cvgmt.sns.it/papers/emiman03/
SOME PROPERTIES OF THE DISTANCE FUNCTION AND A
CONJECTURE OF DE GIORGI
MANOLO EMINENTI AND CARLO MANTEGAZZA
ABSTRACT. In the paper [2] Ennio De Giorgi conjectured that any compact n­
dimensional regular submanifold M of
n¡ m, moving by the gradient of the func-
tional ¢
M
1 £¥¤¦ k
M
¤2
d§ n
,
where M is the square of the distance function from the submanifold M and § n
is the n­dimensional Hausdorff measure in
n¡ m, does not develop singularities
in finite time provided k is large enough, depending on the dimension n.
We prove this conjecture by means of the analysis of the geometric properties of
the high derivatives of the distance function from a submanifold of the Euclidean

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics