<div class="csl-bib-body">
<div class="csl-entry">Le, M. T. (2024, April 12). <i>Determining functions via their descent modulus</i> [Presentation]. Geometry Group Seminar, Cluj-Napoca, Romania.</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/201621
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dc.description.abstract
It was established in [1] that Lipschitz inf-compact functions are uniquely determined by their local slope and critical values. Compactness played a paramount role in this result, particularly ensuring the existence of critical points. In this talk, we establish a determination result for merely bounded from below functions in complete metric spaces, by adding an assumption controlling the asymptotic behavior. This assumption is trivially fulfilled if a function is inf-compact. Additionally, our result is valid for a wide range of descent moduli including the (De Giorgi) local slope, global slope and average descent operators.
[1] A. Daniilidis and D. Salas, A determination theorem in terms of the metric slope, Proc. Amer. Math. Soc. 150 (2022), 4325–4333.
[2] A. Daniilidis, T. M. Le and D. Salas, Metric compatibility and determination in complete metric spaces, arXiv:2308.14877.
