Zobrazeno 1 - 10
of 307
pro vyhledávání: '"Zhu, Jonathan A."'
Autor:
Naff, Keaton, Zhu, Jonathan J.
We prove ``half-space" intersection properties in three settings: the hemisphere, half-geodesic balls in space forms, and certain subsets of Gaussian space. For instance, any two embedded minimal hypersurfaces in the sphere must intersect in every cl
Externí odkaz:
http://arxiv.org/abs/2401.09669
Autor:
Hirsch, Sven, Zhu, Jonathan J.
We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by Schulze a
Externí odkaz:
http://arxiv.org/abs/2310.08005
We prove that curve shortening flow on the round sphere displays sharp chord-arc improvement, precisely as in the planar setting (Andrews and Bryan, Comm. Anal. Geom., 2011). As in the planar case, the sharp estimate implies control on the curvature,
Externí odkaz:
http://arxiv.org/abs/2310.02649
Autor:
Langford, Mat, Zhu, Jonathan J.
We introduce a reflected chord-arc profile for curves with orthogonal boundary condition and obtain a chord-arc estimate for embedded free boundary curve shortening flows in a convex planar domain. As a consequence, we are able to prove that any such
Externí odkaz:
http://arxiv.org/abs/2302.14258
Autor:
Peng, Tai-Quan, Zhu, Jonathan J. H.
Timestamps in digital traces include significant detailed information on when human behaviors occur, which is universally available and standardized in all types of digital traces. Nevertheless, the concept of time is under-explicated in empirical st
Externí odkaz:
http://arxiv.org/abs/2301.05996
We investigate the formation of musical preferences of millions of users of the NetEase Cloud Music (NCM), one of the largest online music platforms in China. We combine the methods from complex networks theory and information sciences within the con
Externí odkaz:
http://arxiv.org/abs/2212.13139
Autor:
Naff, Keaton, Zhu, Jonathan J.
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ball. These monotonicity formulae involve an energy-like integral over s
Externí odkaz:
http://arxiv.org/abs/2210.03263
Autor:
Naff, Keaton, Zhu, Jonathan J.
We prove a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in hyperbolic space, in any dimension and codimension. In certain cases, we also prove the corresponding estimate in the sphere. Our estim
Externí odkaz:
http://arxiv.org/abs/2206.08302
Autor:
Zhu, Jonathan J.
We observe that the $k$-dimensional width of an $n$-ball in a space form is given by the area of an equatorial $k$-ball. We also investigate related lower bounds for the area of a free boundary minimal submanifold in a space form ball.
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Externí odkaz:
http://arxiv.org/abs/2203.10031
We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existence of nontrivial, smooth, almost properly embedded surfaces with any
Externí odkaz:
http://arxiv.org/abs/2111.09924