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Local Regularity Properties of Almost- and Quasiminimal Sets with a Sliding Boundary Condition
 
Guy David Université Paris-Sud, Orsay, France
A publication of the Société Mathématique de France
Local Regularity Properties of Almost- and Quasiminimal Sets with a Sliding Boundary Condition
Softcover ISBN:  978-2-85629-906-7
Product Code:  AST/411
List Price: $97.00
AMS Member Price: $77.60
Please note AMS points can not be used for this product
Local Regularity Properties of Almost- and Quasiminimal Sets with a Sliding Boundary Condition
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Local Regularity Properties of Almost- and Quasiminimal Sets with a Sliding Boundary Condition
Guy David Université Paris-Sud, Orsay, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-906-7
Product Code:  AST/411
List Price: $97.00
AMS Member Price: $77.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 4112019; 380 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 4112019; 380 pp
MSC: 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.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.