Extremal Problems in Minkowski Space Related to Minimal Networks
نویسنده
چکیده
We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan [FLM]: Is there an upper bound polynomial in n for the largest cardinality of a set S of unit vectors in an n-dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that |S| ≤ 2n and that equality holds iff the space is linearly isometric to l ∞ , the space with an n-cube as unit ball. We also remark on similar questions raised in [FLM] that arose out of the study of singularities in length-minimizing networks in Minkowski spaces.
منابع مشابه
$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$
Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...
متن کاملm-Projections involving Minkowski inverse and range symmetric property in Minkowski space
In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...
متن کاملTranslation Surfaces of the Third Fundamental Form in Lorentz-Minkowski Space
In this paper we study translation surfaces with the non-degenerate third fundamental form in Lorentz- Minkowski space $mathbb{L}^{3}$. As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form $III$ on the surface.
متن کاملOn Rectifying Curves as Centrodes and Extremal Curves in the Minkowski 3-space
In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3-space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying curves are not the extremal curves and giv...
متن کاملA Novel Image Structural Similarity Index Considering Image Content Detectability Using Maximally Stable Extremal Region Descriptor
The image content detectability and image structure preservation are closely related concepts with undeniable role in image quality assessment. However, the most attention of image quality studies has been paid to image structure evaluation, few of them focused on image content detectability. Examining the image structure was firstly introduced and assessed in Structural SIMilarity (SSIM) measu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996