The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 871–882 | Cite as

Perimeter under Multiple Steiner Symmetrizations

  • Almut BurchardEmail author
  • Gregory R. Chambers


Steiner symmetrization in n linearly independent directions transforms every compact subset of \(\mathbb {R}^{n}\) into a set of finite perimeter.


Hausdorff Distance Nonnegative Continuous Function Dimensional Hausdorff Measure Coordinate Hyperplane Independent Direction 
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This work was partially supported by an NSERC Discovery Grant (Burchard) and an NSERC Alexander Graham Bell Canada Graduate Scholarship (Chambers). We would also like to thank Luigi Ambrosio for the proof of Lemma 5.


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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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