General $L_p$ affine isoperimetric inequalities
By Christoph Haberl, Franz E. Schuster. 2008
387 citations recorded by the source corpus.
Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.
Subfields: Applied Mathematics, Pharmacology
View Paper: https://www.semanticscholar.org/paper/269990689da135989ca7fa3105f3e25003b36717
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In Applied Mathematics
- Yiming Zhao
- Monika Ludwig
- Deane Yang
- Gaoyong Zhang
- Erwin Lutwak
- Yong Huang
- Christoph Haberl
- Franz E. Schuster
In Pharmacology
- Monika Ludwig
- Christoph Haberl
- Gaoyong Zhang
- Deane Yang
- Erwin Lutwak
- Ai-jun Li
- Gangsong Leng
- Lukas Parapatits
Citations in the corpus
- Asymmetric affine Lp Sobolev inequalities (2009, background): “While the geometric inequalities behind the ane Zhang‐Sobolev inequality and inequality (1.3) for p = 1 are the same, a new ane isoperimetric inequality recently established by the authors [ 13 ] is needed to establish inequality (1.3) for p > 1. We will apply this inequality to convex bodies (assoc”
- The logarithmic Minkowski problem (2012, positive): “These were then strengthened by Haberl et al in [25–27].”
- 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.”
- A new proof of the Orlicz Busemann-Petty centroid inequality (2011, methodology): “This extension is motivated by asymmetric concepts within the Lp Brunn-Minkowski theory developed by Ludwig [14], Haberl and Schuster [9, 11], and Ludwig and Reitzner [16].”
- Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, neutral): “The L p Brunn-Minkowski theory is an extension of the classical Brunn-Minkowski theory, see [40, 47, 51, 54, 56, 57, 60, 63, 73].”
- Minkowski Areas and Valuations (2010, background): “In recent years, such affine functions on convex bodies have attracted increased interest (see, for example, [10, 14, 18, 21, 25, 26, 41, 42, 43, 45, 46, 56, 57]).”