[1] Aleksandrov A D. Zur Theorie der gemischten Volumina von konvexen Körper, III: Die Erweiterung zweier Lehrsatze Minkowskis Über die konvexen Polyeder auf beliebige konvexe Flächen (in Russian). Mat Sbornik (NS), 1938, 3: 27-46  [2] Alfonseca M A, Nazarov F, Ryabogin D, et al. Two results on the homothety conjecture for convex bodies of floation on the plane. 2024, preprint.  [3] Alfonseca M A, Ryabogin D, Stancu A, Yaskin V. On flotation, stability and related questions: A survey. 2024, submitted.  [4] Bárány I, Larman D G. Convex bodies, economic cap coverings, random polytopes. Mathematika, 1988, 35: 274-291  [5] Barker J A, Larman D G. Determination of convex bodies by certain sets of sectional volumes. Discrete Mathematics, 2001, 241: 79-96  [6] Böröczky K, Lutwak E, Yang D, Zhang G. The logarithmic Minkowski problem. J Amer Math Soc, 2013, 26: 831-852  [7] Busemann H, Petty C M. Problems on convex bodies. Math Scand, 1956, 4: 88-94  [8] Dupin C. Applications de Géométrie et de Méchanique la Marine, aux Ponts et Chaussées, etc. Paris, 1822. available at https://books.google.com/books?id=QKL2SpP0JuMC  [9] Kurusa á, ódor T. Characterizations of balls by sections and caps. Beit zur Alg und Geom, 2015, 56: 459-471  [10] Langharst D, Ulivelli J. The (self-similar, variational) rolling stones. Int Math Res Not, 2024, 2024(11): 9178-9193  [11] Leichtweiss K. Über eine formel Blaschkes zur affinoberfläche. Studia Sci Math Hungar, 1986, 21: 453-474  [12] Leichtweiss K. On a problem of W.J. Firey in connection with the characterization of spheres. Mathematica Pannonica, 1995, 6: 67-75  [13] Lutwak E. Dual mixed volumes. Pacific J Math, 1975, 58: 531-538  [14] Reuter C. Local fixed point results for centroid body operators. arXiv:2312.10574  [15] Ryabogin D. A negative answer to Ulam's problem 19 from the Scottish Book. Ann of Math (2), 2022, 195: 1111-1150  [16] Schneider R. Convex Bodies: The Brunn-Minkowski Theory. Cambridge: Cambridge University Press, 2013  [17] SchÜtt C, Werner E. The convex floating body, Math Scand, 1990, 66: 275-290  [18] Stancu A. The floating body problem. Bull London Math Soc, 2006, 38: 839-846  [19] Xi D, Yang D, Zhang G, Zhao Y. The $L_p$ chord Minkowski problem. Adv Nonlinear Studies, 2023, 23: 1-22  [20] Yaskin V. Unique determination of convex polytopes by non-central sections. Math Ann, 2011, 349: 647-655  [21] Yaskin V, Yaskina M. Thick sections of convex bodies. Adv in Appl Math, 2015, 71: 174-189  [22] Yaskin V, Zhang N. Non-central sections of convex bodies. Israel J Math, 2017, 220: 763-790 |