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Some generalizations on affine invariant points


Author: Natalia Jonard-Pérez
Journal: Proc. Amer. Math. Soc. 148 (2020), 5299-5311
MSC (2010): Primary 52A20, 54B20, 54H15, 57S20
DOI: https://doi.org/10.1090/proc/15229
Published electronically: September 11, 2020
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Abstract: In this note we prove a more general (and topological) version of Grünbaum's conjecture about affine invariant points. As an application of our result we show that if we consider the action of the group of similarities, Grünbaum's conjecture remains valid in other families of convex sets (not necessarily convex bodies).


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Natalia Jonard-Pérez
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México
Email: nat@ciencias.unam.mx

DOI: https://doi.org/10.1090/proc/15229
Received by editor(s): January 2, 2020
Received by editor(s) in revised form: February 25, 2020
Published electronically: September 11, 2020
Additional Notes: The author was partially supported by grants IN115819 (PAPIIT, UNAM, México) and 252849 (CONACYT-SEP, México).
Communicated by: Deane Yang
Article copyright: © Copyright 2020 American Mathematical Society