General affine surface areas

By Monika Ludwig. 2009

212 citations recorded by the source corpus.

Abstract Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for L ϕ affine surface areas are established.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/02a29611c12cb8b837e8b1b770754c1721917233

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In Applied Mathematics

1. Yiming Zhao
2. Deping Ye
3. Yong Huang
4. Deane Yang
5. Gaoyong Zhang
6. Erwin Lutwak
7. K. Boroczky
8. Sudan Xing

In Computational Mechanics

1. Christoph Haberl
2. Sudan Xing
3. Dongmeng Xi
4. Yong Huang
5. Richard J. Gardner
6. Jian Lu
7. Baocheng Zhu
8. Deping Ye

Citations in the corpus

• The Minkowski problem in Gaussian probability space (2020, background): “Due to limit of space, we mention only a selection of beautiful results in this area, [10,12,33,34,54,56,60,61,63,65, 69,70,72] and refer the interested readers to Schneider’s book [66] for more details.”
• The even Orlicz-Minkowski problem (2010, methodology): “A byproduct is a new approach to the solution of the classical Minkowski problem.”
• Dual Orlicz-Brunn-Minkowski theory (2014, methodology): “Recently, progress towards an Orlicz–Brunn–Minkowski theory was made by Lutwak, Yang and Zhang [43,44] and Ludwig [32].”
• The L-Minkowski problem for −n < p < 1 (2017, background): “[57] M. Ludwig, M. Reitzner, A classification of SL(n) invariant valuations.”
• New Orlicz affine isoperimetric inequalities (2014, background): “Ludwig in [21] defined general affine surface areas involving general convex and concave functions, which are natural extensions of the Lp affine surface area based on formula (1.”
• The Dual Orlicz–Minkowski Problem (2017, methodology): “This new theory started from the works of Lutwak, Yang and Zhang [35, 36] and Ludwig [27], and was greatly pushed forward by Gardner, Hug and Weil [12] and independently by Xi, Jin and Leng [46], due to the discovery of the Orlicz addition of convex bodies.”
• A flow method for the dual Orlicz–Minkowski problem (2020, background): “They have attracted great attention from many researchers, see for example [11, 20, 22, 27, 29, 30, 32, 33, 34, 36, 43, 45, 51, 53, 55, 56, 58, 60, 63, 66, 69] and references therein.”
• Divergence for s-concave and log concave functions (2013, background): “, [23], [37], [39], [40], [50], [61], [62], [66]-[70] for more information on Lp-affine surface area for convex bodies.”
• The logarithmic Minkowski problem (2012, unknown): “[4], [19], [37], [38], [50], [51], [54], and [59].”