
Softcover ISBN: | 978-2-85629-906-7 |
Product Code: | AST/411 |
List Price: | $97.00 |
AMS Member Price: | $77.60 |

Softcover ISBN: | 978-2-85629-906-7 |
Product Code: | AST/411 |
List Price: | $97.00 |
AMS Member Price: | $77.60 |
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Book DetailsAstérisqueVolume: 411; 2019; 380 ppMSC: Primary 49
The author studies the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set \(E\) are defined as \(F =\varphi_{1}(E)\), where \(\{\varphi_{t}\}\) is a one parameter family of continuous mappings defined on \(E\), and that preserve a given collection of boundary pieces.
The author generalizes known interior regularity results, and, in particular, he shows that the quasiminimal sets are locally Ahlfors-regular, rectifiable, and, sometimes, uniformly rectifiable; that these classes are stable under limits; and that for almost- minimal sets, the density of Hausdorff measure in balls centered on the boundary is almost nondecreasing.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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The author studies the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set \(E\) are defined as \(F =\varphi_{1}(E)\), where \(\{\varphi_{t}\}\) is a one parameter family of continuous mappings defined on \(E\), and that preserve a given collection of boundary pieces.
The author generalizes known interior regularity results, and, in particular, he shows that the quasiminimal sets are locally Ahlfors-regular, rectifiable, and, sometimes, uniformly rectifiable; that these classes are stable under limits; and that for almost- minimal sets, the density of Hausdorff measure in balls centered on the boundary is almost nondecreasing.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.