Valuations and Busemann{Petty Type Problems

By Franz E. Schuster. 2008

101 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b86fb06794f18625806351de08087c96a55aa903

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yiming Zhao
2. Yong Huang
3. Deane Yang
4. Gaoyong Zhang
5. K. Boroczky
6. Erwin Lutwak
7. Monika Ludwig
8. Franz E. Schuster

In Geometry and Topology

1. Yiming Zhao
2. Monika Ludwig
3. Yong Huang
4. Franz E. Schuster
5. Deane Yang
6. Gaoyong Zhang
7. K. Boroczky
8. Erwin Lutwak

Citations in the corpus

• Minkowski Areas and Valuations (2010, background): “of elementary mixed volumes, valuations have become a critical notion (see [27, 31, 47] and see [1, 2, 3, 4, 5, 6, 11, 15, 29, 30, 49, 51, 52, 53] for some of the more recent contributions).”
• Fisher information and matrix-valued valuations (2011, result): “See [24, 27] for information on the classical theory of valuations on convex sets and [1–5,9,11,16,19–22,28– 31, 33, 34, 43–45] for some of the more recent results.”
• 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.”
• The dual Minkowski problem for symmetric convex bodies (2017, background): “[47] F.E. Schuster & T. Wannerer, GL(n) contravariant Minkowski valuations, Trans.”
• Crofton Measures and Minkowski Valuations (2010, methodology): “In the following we give a few well-known examples of Minkowski valuations in MVal (for additional examples, see, e.g., [24, 31, 48 ]):”
• 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.”
• 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.”
• Valuations and Surface Area Measures (2014, unknown): “[2–6, 9, 13–15, 20–25, 34, 39–41]).”