Minkowski Areas and Valuations

By Monika Ludwig. 2010

135 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c746f24ea6afd7eccc47e535848d43a659889e0e

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In Applied Mathematics

Citations in the corpus

Harmonic Analysis of Translation Invariant Valuations (2010, background): “sp. ϑ∈ SO(n)). In their book on geometric probability, Klain and Rota [31] pose the problem to classify all ”invariant” bivaluations. First such classiﬁcation results were obtained recently by Ludwig [36]. In Section 6 we obtain a description of all continuous translation biinvariant bivaluations wh”
Anisotropic fractional perimeters (2013, unknown): “[17,25]) and moment bodies in the theory of valuations on convex bodies (see [20, 23, 24]).”
Valuations and Surface Area Measures (2014, unknown): “[2–6, 9, 13–15, 20–25, 34, 39–41]).”
Stronger versions of the Orlicz-Petty projection inequality (2011, background): “onsoGutierrez, J. Bastero, J. Bernues [1], R.J. Gardner, G. Zhang [14], C. Haberl, F.E. Schuster [21, 22], C. Haberl, F.E. Schuster, J. Xio [23], E. Lutwak, D. Yang, G. Zhang [31, 33, 34], M. Ludwig [27, 28], M. Schmuckenschlager [40], F.E. Schuster, T. Wannnerer [41], J. Xiao [42]). The notion of p”
Existence of solutions to the even dual Minkowski problem (2018, methodology): “It is still being intensively studied, see, for example, Barthe, Guédon, Mendelson & Naor [4], Böröczky & Henk [6], Böröczky-LYZ [8, 9, 10], Henk & Linke [31], Ludwig [38], Ludwig & Reitzner [40], Naor [47], Naor & Romik [48], Paouris & Werner [51], Stancu [61, 62], Xiong [65], Zhu [70], and Zo”
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].”
The Hadwiger Theorem on Convex Functions, I (2020, background): “Interesting new valuations keep arising (see, for example, [8,24,31]) and see [1,2,4,6,7,21,22,29,32,35,36,39] for some recent classification results.”
The Centro-Affine Hadwiger Theorem (2013, background): “ long conjectured property, ﬁnally established in [48]) was crucial for the solution of the aﬃne Plateau problem [72]. Hadwiger type theorems were established also in various other contexts (see e.g. [10,32,33,35, 43,44]). Of particular importance are classiﬁcation theorems of body valued valuations”
Minkowski valuations and generalized valuations (2015, background): “In a more recent influential article, Ludwig [41] coined the name Minkowski valuations for such maps and started a line of research concerned with the classification of Minkowski valuations intertwining linear transformations, see [1, 2, 30, 40, 42, 61, 65].”