منابع مشابه
Adding one handle to half-plane layers
In this paper, we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by their period. These surfaces are constructed by adding a handle to the toroidal half-plane layers defined by H. Karcher. The technics that we use is to solve a Jenkins-Serrin problem over a strip domain and to consider the conjugate minimal surface to the graph.
متن کاملAn Introduction to Upper Half Plane Polynomials
For example, x1 + · · · + xd ∈ Ud (C). This follows from the fact that the upper half plane is a cone, so if σ1, . . . , σd are in the upper half plane then so is their sum. Another example is x1x2 − 1. If σ1 and σ2 are in the upper half plane then σ1σ2 ∈ C \ (0,∞), so σ1σ2 − 1 is not zero. U1 (C) is easily described. It is all polynomials in one variable whose roots are either real, or lie in ...
متن کاملTightness for Smooth and Polyhedral Immersions of the Projective Plane with One Handle
The recent discovery that there is a tight polyhedral immersion of the projective plane with one handle, while there is no smooth tight immersion of the same surface, provides a rare example in low dimensions of a significant difference between smooth and polyhedral surfaces. In this paper the author shows that the obstruction to smoothing the polyhedral model is not local in nature, and descri...
متن کاملA Tight Polyhedral Immersion in Three-space of the Real Projective Plane with One Handle
In 1960, Nicolaas Kuiper showed that every surface can be tightly immersed in three-space except for the real projective plane and the Klein bottle, for which no such immersion exists, and the real projective plane with one handle, for which he could find neither a tight example nor a proof that one does not exist. It was not until more than 30 years later, in 1992, that François Haab proved th...
متن کاملMultiple cracks in an elastic half-plane subjected to thermo-mechanical loading
An analytical solution is presented for the thermoelastic problem of a half-plane with several cracks under thermo mechanical loading using distributed dislocation technique. The uncoupled quasi-static linear thermoelasticity theory is adopted in which the change in temperature, if any, due to deformations is neglected. The stress field in a half-plane containing thermoelastic dislocation is ob...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2010
ISSN: 0022-040X
DOI: 10.4310/jdg/1274707318