منابع مشابه
Simply-connected Nonpositive Curved Surfaces in R3
where |B| is the length of second fundamental form. |B|2 = 4|H|2 − 2K, where H is the mean curvature and K is the Gauss curvature. The curvature of minimal surfaces is nonpositive. Then we exam what is still hold for some minimal surface theorems if extending the minimal condition H ≡ 0 to the surfaces with K ≤ 0 and (1). In 2001, F. Xavier [18] has the following theorem: Theorem [Xavier]. Let ...
متن کاملComplete Properly Embedded Minimal Surfaces in R3
In this short paper, we apply estimates and ideas from [CM4] to study the ends of a properly embedded complete minimal surface 2 ⊂ R3 with finite topology. The main result is that any complete properly embedded minimal annulus that lies above a sufficiently narrow downward sloping cone must have finite total curvature. In this short paper, we apply estimates and ideas from [CM4] to study the en...
متن کاملA Comparative Study between Biharmonic Bézier Surfaces and Biharmonic Extremal Surfaces
Given a prescribed boundary of a Bézier surface, we compare the Bézier surfaces generated by two different methods, i.e., the Bézier surface minimising the biharmonic functional and the unique Bézier surface solution of the biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper, we prov...
متن کاملSomeNewDevelopments of Realization of Surfaces into R3
This paper intends to give a brief survey of the developments on realization of surfaces into R in the last decade. As far as the local isometric embedding is concerned, some results related to the Schlaffli-Yau conjecture are reviewed. As for the realization of surfaces in the large, some developments on Weyl problem for positive curvature and an existence result for realization of complete ne...
متن کاملOn harmonic and biharmonic Bézier surfaces
We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bézier surfaces. The main result we report here is that any biharmonic Bézier surface is fully determined by the boundary control points. We compare the new method, by way of practical example...
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ژورنال
عنوان ژورنال: Selecciones Matemáticas
سال: 2020
ISSN: 2411-1783
DOI: 10.17268/sel.mat.2020.01.08