Abstract
We show that the copolarity of pseudo-cones has properties analogous to those of the usual polarity of convex bodies.
References
- S. Artstein-Avidan, S. Sadovsky, K. Wyczesany: A zoo of dualities, J. Geom. Analysis 33/8 (2023), art. no. 8, 40p.https://doi.org/10.1007/s12220-023-01302-0Google Scholar
- K. J. Böröczky, R. Schneider: A characterization of the duality mapping for convex bodies, Geom. Funct. Analysis 18/3 (2008) 657–667.https://doi.org/10.1007/s00039-008-0676-5Google Scholar
- D. Hug: Curvature relations and affine surface area for a general convex body and its polar, Results Math. 29 (1996) 233–248.https://doi.org/10.1007/BF03322221Google Scholar
- D. Hug, W. Weil: Lectures on Convex Geometry, Springer, Cham (2020).https://doi.org/10.1007/978-3-030-50180-8Google Scholar
- F. J. Kaltenbach: Asymptotisches Verhalten zufälliger konvexer Polytope, Dissertation, University of Freiburg (1990).Google Scholar
- D. Laugwitz: Differentialgeometrie in Vektorräumen, Vieweg, Braunschweig (1965).Google Scholar
- A.-M. Li, U. Simon, G. Zhao: Global Affine Differential Geometry of Hypersurfaces, De Gruyter, Berlin (1993).Google Scholar
- V. Oliker, U. Simon: Affine Geometry and Polar Hypersurfaces, in: Analysis and Geometry, B. Fuchssteiner et al. eds., Bibliographisches Institut, Mannheim (1992), 87–112.Google Scholar
- A. Rashkovskii: Copolar convexity, Ann. Polon. Math. 120 (2017) 83–95.https://doi.org/10.4064/ap170217-4-9Google Scholar
- H. Rund: The Differential Geometry of Finsler Spaces, Springer, Berlin (1959).https://doi.org/10.1007/978-3-642-51610-8Google Scholar
- E. Salkowski: Affine Differentialgeometrie, De Gruyter, Berlin (1934).https://doi.org/10.1515/9783111338279Google Scholar
- R. Schneider: Zur affinen Differentialgeometrie im Großen, Math. Zeitschrift 101 (1967) 375–406.https://doi.org/10.1007/BF01109803Google Scholar
- R. Schneider: Convex Bodies: The Brunn-Minkowski Theory, 2nd ed., Encyclopedia of Mathematics and Its Applications Vol. 151, Cambridge University Press, Cambridge (2014).Google Scholar
- R. Schneider: Pseudo-cones, Adv. Appl. Math. 155 (2024), art. no. 102657, 22p.https://doi.org/10.1016/j.aam.2023.102657Google Scholar
- U. Simon: Zur Relativgeometrie: Symmetrische Zusammenhänge auf Hyperflächen, Math. Zeitschrift 106 (1968) 36–46.https://doi.org/10.1007/BF01137970Google Scholar
- Y. Xu, J. Li, G. Leng: Dualities and endomorphisms of pseudo-cones, Adv. Appl. Math. 142 (2023), art. no. 102434, 31p.https://doi.org/10.1016/j.aam.2022.102434Google Scholar
Suggested citation
Published by Heldermann Verlag, 2025. Rights now held by Banach Press LLC.
