Crofton Measures and Minkowski Valuations

By Franz E. Schuster. 2010

178 citations recorded by the source corpus.

A description of continuous rigid motion compatible Minkowski valuations is established. As an application, we present a Brunn-Minkowski type inequality for intrinsic volumes of these valuations.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/e696ce709f8549310df9c9d3b605a11fa526781d

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In Applied Mathematics

Citations in the corpus

The dual Minkowski problem for negative indices (2017, background): “See, e.g., Haberl [19], Haberl & Ludwig [20] ,Haberl & Parapatits [21,22], Ludwig [27,28], Ludwig & Reitzner [29], Schuster [39, 40], Schuster & Wannerer [41] and the references therein for important valuations and their characterizations in the theory of convex bodies.”
Projection bodies in complex vector spaces (2011, background): “See [6, 18, 24, 25, 26, 27, 28, 44, 46, 47, 48] for more information on Minkowski valuations.”
The log-Brunn-Minkowski inequality (2012, unknown): “, [1,56,61] for some recent developments).”
The dual Minkowski problem for symmetric convex bodies (2017, background): “[47] F.E. Schuster & T. Wannerer, GL(n) contravariant Minkowski valuations, Trans.”
Kinematic formulas for tensor valuations (2014, background): “We refer to [1, 2, 24, 31, 44, 46] to cite just a few papers in this direction.”
On the L dual Minkowski problem (2018, background): “See, for example, Alesker [1], Haberl [26], Haberl & Parapatits [28], Ludwig [42, 43, 45, 46], Ludwig & Reitzner [47], Schuster [59, 60], Schuster & Wannerer [61] and the references therein for important valuations in the theory of convex bodies.”
Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, unknown): “, [4]–[7], [12], [37]–[39], [47]–[51], and [76]–[77]).”
Difference bodies in complex vector spaces (2012, background): “Some results on Minkowksi valuations not described in this paper can be found, for instance, in [18, 19, 21, 32, 33, 42, 43, 45].”
Harmonic Analysis of Translation Invariant Valuations (2010, methodology): “The special case of Theorem 3 for even Minkowski valuations was recently established by other methods by the third author [51].”
R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, unknown): “, [5], [7] - [11], [13], [14], [17] - [24], [26], [28], [31] - [34], [37], [38] - [46], [50]), is now a central part of modern convex geometry.”
Existence of solutions to the even dual Minkowski problem (2018, methodology): “Valuations have been the objects of many recent works, see, for example, Haberl [28], Haberl & Parapatits [29], Ludwig [37, 39], Ludwig & Reitzner [40], Schuster [57, 58], Schuster & Wannerer [59] and the references therein.”