We establish an equivalence form of the dual Brunn-Minkowski inequality for volume differences, which was established in Geom. Dedicata 145 (2010) 169-180.

Contact details are reproduced from the original publication and may be historical.

Chang-Jian Zhao

Dept. of Mathematics, College of Science, China Jiliang University, Hangzhou 310018, P.R.China

chjzhao@yahoo.com.cn

Wing-Sum Cheung

Dept. of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

wscheung@hku.hk
  1. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, Cambridge (1993).https://doi.org/10.1017/CBO9780511526282Google Scholar
  2. E. Lutwak: Dual mixed volumes, Pacific J. Math. 58 (1975) 531–538.https://doi.org/10.2140/pjm.1975.58.531Google Scholar
  3. R. J. Gardner: Geometric Tomography, Cambridge Univ. Press, Cambridge (1995).Google Scholar
  4. E. Lutwak: Intersection bodies and dual mixed volumes, Adv. Math. 71 (1988) 232–261.https://doi.org/10.1016/0001-8708(88)90077-1Google Scholar
  5. G. S. Leng: The Brunn-Minkowski inequality for volume differences, Adv. Appl. Math. 32 (2004) 615–624.https://doi.org/10.1016/S0196-8858(03)00095-2Google Scholar
  6. C. Zhao, W. Cheung: An equivalence form of the Brunn-Minkowski inequality for volume differences, J. Korean Math. Soc. 44 (2007) 1373–1381.https://doi.org/10.4134/JKMS.2007.44.6.1373Google Scholar
  7. S. Lv: Dual Brunn-Minkowski inequality for volume differences, Geom. Dedicata 145 (2010) 169–180.https://doi.org/10.1007/s10711-009-9414-xGoogle Scholar
  8. E. F. Beckenbach, R. Bellman: Inequalities, 2nd Ed., Springer, Berlin (1965).https://doi.org/10.1007/978-3-662-35199-4Google Scholar

C.-J. Zhao, W.-S. Cheung. “An Equivalence of Dual Brunn-Minkowski Inequality for Volume Differences.” Journal of Convex Analysis 20 (2013), No. 2, 475–481. https://doi.org/10.68381/jca20028