Valuations on Sobolev spaces

By Monika Ludwig. 2012

90 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/277708be65d1597ddb638dc4563e1ca44c70f8e5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A homogeneous decomposition theorem for valuations on convex functions (2019, methodology): “Classification results were obtained for Lp and Sobolev spaces [24–27, 29, 38, 39], spaces of quasi-convex functions [12, 13], of Lipschitz functions [17], of definable functions [4] and on Banach lattices [37].”
Valuations on Convex Functions (2017, background): “For Sobolev spaces [21,23,27] and Lp spaces [24,32,33] complete classifications for valuations intertwining the SL(n) were established.”
Valuations on convex functions and convex sets and Monge–Ampère operators (2017, background): “he notion of valuation have been suggested. One of these recent generalizations is the notion of valuation on a class of functions introduced and studied by M. Ludwig and others, see e.g. [14], [15], [16], [10], [21], [22]. Let us give a deﬁnition of valuation on convex functions which is relevant f”
The Hadwiger Theorem on Convex Functions, I (2020, background): “The first classification results were obtained for Lp and Sobolev spaces, for Lipschitz functions and for definable functions (see, for example, [5, 19, 29, 33, 34, 46]).”
Quermassintegrals of quasi-concave functions and generalized Prékopa–Leindler inequalities (2012, background): “Let us mention that recently some characterizations of valuations in various function spaces have been found, see for instance [23, 35].”
On the L dual Minkowski problem (2018, background): “See, for example, Barthe, Guédon, Mendelson & Naor [4], Böröczky & Henk [7], Böröczky, Lutwak, Yang & Zhang [9–11], Henk & Linke [29], Ludwig [44], Ludwig & Reitzner [47], Naor [54], Naor & Romik [55], Paouris & Werner [56], Stancu [62,63], Xiong [65], Zhu [70], and Zou & Xiong [73].”
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”