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We shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called 'flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When equality holds in this inequality, we show that all the ends are embedded. Moreover, we shall give new examples for which equality holds.
Gastrointestinal hormones including gastric inhibitory polypeptide (GIP), glucagon-like peptide (GLP)-1, and GLP-2 are secreted immediately after meal ingestion, and GIP and GLP-2 have been shown to regulate bone turnover. We hypothesize that endogenous GLP-1 may also be important for control of skeletal homeostasis. We investigated the role of GLP-1 in the… (More)
We shall investigate maximal surfaces in Minkowski 3-space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show that they satisfy an Osserman-type inequality.
In this work we give a method for constructing a one-parameter family of complete CMC-1 (i.e. constant mean curvature 1) surfaces in hyperbolic 3-space that correspond to a given complete minimal surface with finite total curvature in Euclidean 3-space. We show that this one-parameter family of surfaces with the same symmetry properties exists for all given… (More)
We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges. Moreover, it is deeply related to the behavior of the Gaussian curvature of a surface near cuspidal edges and swallowtails.
A complete surface of constant mean curvature 1 (CMC-1) in hyperbolic 3-space with constant curvature −1 has two natural notions of " total curvature " — one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute curvature which is the total absolute… (More)
In this work, complete constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space with total absolute curvature at most 4π are classified. This classification suggests that the Cohn-Vossen inequality can be sharpened for surfaces with odd numbers of ends, and a proof of this is given.
Corosolic acid (CRA), a constituent of Banaba leaves, has been reported to exert anti-hypertension, anti-hyperinsulinemia, anti-hyperglycemia, and anti-hyperlipidemia effects as well as to induce anti-inflammatory and anti-oxidative activities. The aim of this study was to investigate the inhibitory effects of CRA on the development of obesity and hepatic… (More)
The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the… (More)