Xuwen Zhang (Universität Frankfurt):
FORMULATING CAPILLARY SURFACES IN THE CONTEXT OF VARIFOLDS
Zeit und Ort
Dienstag, 5.12.23, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
Zusammenfassung
Capillary surface is a fundamental geometric object, describing a particular boundary behavior of surface in a given container. In some recent works of Kagaya-Tonegawa (Hiroshima Math. J. 47(2): 139-153, 2017. https://doi.org/10.32917/hmj/1499392823), De Masi-De Philippis (https://doi.org/10.48550/arXiv.2111.09913), weak capillary surfaces are formulated, using the language of varifolds, and named ”pair of varifolds with fixed contact angle condition”.\n\nIn this talk, we will discuss some recent development in this direction, and prove a strong boundary maximum principle for a specific class of pairs of varifolds with fixed contact angle, which generalizes Li-Zhou’s boundary maximum principle for free boundary varifolds (Comm.\nAnal. Geom. (29): 1509–1521, 2021. https://doi.org/10.4310/CAG.2021.v29.n6.a7). The similar results in the context of rectifiable cones will be discussed as well. If time permits, we will also discuss some applications of the weak formulation, including the establishment of the\nSimon-type monotonicity identities as well as the Li-Yau-type inequalities.