共查询到20条相似文献,搜索用时 0 毫秒
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Mu-Tao Wang 《Transactions of the American Mathematical Society》2003,355(1):265-271
Let be a minimal submanifold of that can be represented as the graph of a smooth map . We apply a formula that we derived in the study of mean curvature flow to obtain conditions under which must be an affine subspace. Our result covers all known ones in the general case. The conditions are stated in terms of the singular values of .
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Yves Diers 《Applied Categorical Structures》1996,4(2-3):329-341
The category of algebraic sets is defined in a straightforward way for any algebraic theory . It is a concrete, complete and cocomplete category dually equivalent to a full reflective subcategory of the category of -algebras. For the algebraic theory of commutative algebras over a field K, we get the algebraic sets over K. 相似文献
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Artem N. Shevlyakov 《代数通讯》2017,45(9):3757-3767
A semigroup S is called an equational domain if any finite union of algebraic sets over S is algebraic. We give some necessary and su?cient conditions for a completely simple semigroup to be an equational domain. 相似文献
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We consider three generalizations of the isoperimetric problem to higher codimension and provide results on equilibrium, stability, and minimization. 相似文献
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We show a Bernstein theorem for minimal graphs of arbitrary dimension and codimension under a bound on the slope that improves
previous results and is independent of the dimension and codimension. The proof depends on the regularity theory for the harmonic
Gauss map and the geometry of Grassmann manifolds.
Received: September 25, 1998 / Accepted: October 23, 1998 相似文献
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Marcos Dajczer 《Bulletin of the Brazilian Mathematical Society》1992,23(1-2):67-77
Given an isometric immersionf:M
n
→ ℝ
N
into Euclidean space, we provide sufficient conditions onf so that any 1-regular isometric immersion ofM
n
into ℝ
N+1
is necessarily obtained as a composition off with a local isometric immersion ℝ
N
⊃U → ℝ
N+1
. This result has several applications. 相似文献
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Yves Diers 《Journal of Geometry》1999,65(1-2):54-76
For an arbitrary algebraic theory T and a prescribed T-algebraL, the geometrical category AfAlgSet(L) of affine algebraic sets over the affine lineL is build up. It is proved to be dually equivalent to the category FcAlg(L) of functional T-algebras overL. The Galois theory ofL is defined and a Galois duality established. These geometrical categories are characterized up to an equivalence of categories. 相似文献
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张勇 《中国科学A辑(英文版)》2003,46(5):593-599
In this paper,we study the dynamics of minimal rambling sets with codimension one dominatedsplittings 相似文献
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Paola Pozzi 《Mathematical Methods in the Applied Sciences》2007,30(11):1243-1281
We consider the evolution of parametric curves by anisotropic mean curvature flow in ?n for an arbitrary n?2. After the introduction of a spatial discretization, we prove convergence estimates for the proposed finite‐element model. Numerical tests and simulations based on a fully discrete semi‐implicit stable algorithm are presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Paola Pozzi 《PAMM》2008,8(1):10849-10850
We present recent progress in the study of the anisotropic mean curvature flow in higher codimension. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We prove existence theorems for two-dimensional, noncompact, complete minimal surfaces in ℝn of annular type, which span a given contour and have a finite total curvature end and prescribed asymptotical behavior. For
arbitrary rectifiable Jordan curves, we show the existence of such surfaces with a flat end, i.e., within a bounded distance
from a 2-plane. For more restricted classes of curves, we prove the existence of minimal surfaces with higher multiplicity
flat ends as well as of surfaces with polynomial-type nonflat ends.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 17, Differential and Functional Differential Equations. Part 3, 2006. 相似文献
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K. K. Karchyauskas 《Journal of Mathematical Sciences》1982,19(3):1253-1257
In this paper there are announced several homotopy theorems on algebraic subsets of complex projective spaces. Some of the theorems generalize and refine results of the preceding note of the author (RZhMat, 1978, 5A531). It is also asserted that any -dimensional complex affine algebraic set has the homotopy type of a finite -dimensional cellular space. A generalization is given, in two versions, of a theorem of Bart-Larsen (RZhMat, 1973, 7A587).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 83, pp. 67–72, 1979. 相似文献
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We introduce a new notion of a harmonic measure for a d-dimensional set in with , that is, when the codimension is strictly bigger than 1. Our measure is associated with a degenerate elliptic PDE, it gives rise to a comprehensive elliptic theory, and, most notably, it is absolutely continuous with respect to the d-dimensional Hausdorff measure on reasonably nice sets. This note provides general strokes of the proof of the latter statement for Lipschitz graphs with small Lipschitz constant. 相似文献