Hausdorff Dimension and Non-degenerate Families of Projections

  title={Hausdorff Dimension and Non-degenerate Families of Projections},
  author={E. J{\"a}rvenp{\"a}{\"a} and M. J{\"a}rvenp{\"a}{\"a} and T. Keleti},
  journal={The Journal of Geometric Analysis},
  • E. Järvenpää, M. Järvenpää, T. Keleti
  • Published 2014
  • Mathematics
  • The Journal of Geometric Analysis
  • We study parameterized families of orthogonal projections for which the dimension of the parameter space is strictly less than that of the Grassmann manifold. We answer the natural question of how much the Hausdorff dimension may decrease by verifying the best possible lower bound for the dimension of almost all projections of a finite measure. We also show that a similar result is valid for smooth families of maps from the n-dimensional Euclidean space to the m-dimensional one. 

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