共查询到20条相似文献,搜索用时 15 毫秒
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In this paper we study the generalized mean curvature flow of sets in the sub-Riemannian geometry of Carnot groups. We extend to our context the level sets method and the weak (viscosity) solutions introduced in the Euclidean setting in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow. 相似文献
3.
We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type. 相似文献
4.
The authors consider a family of smooth immersions F(·,t):Mn → Rn+1 of closed hypersurfaces in Rn+1 moving by the mean curvature flow F∈(pt,t)=-H(p,t)·ν(p,t) for t ∈ [0,T).They show that if the norm of the second fundamental form is bounded above by some power of mean curvature and the certain subcritical quantities concerning the mean curvature integral are bounded,then the flow can extend past time T.The result is similar to that in [6-9]. 相似文献
5.
We discuss the motion of noncompact axisymmetric hypersurfaces Γ t evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface. 相似文献
6.
Annalisa Cesaroni 《偏微分方程通讯》2013,38(5):780-801
We consider the long-time behavior of the mean curvature flow in heterogeneous media with periodic fibrations, modeled as an additive driving force. Under appropriate assumptions on the forcing term, we show existence of generalized traveling waves with maximal speed of propagation, and we prove the convergence of solutions to the forced mean curvature flow to these generalized waves. 相似文献
7.
Qi DING 《数学年刊B辑(英文版)》2011,32(1):27-44
In this paper, the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally
symmetric spaces is studied. It is proved that the flow converges to a unique geodesic sphere, i.e., every principle curvature
of the hypersurfaces converges to a same constant under the flow. 相似文献
8.
Henri Anciaux 《Geometriae Dedicata》2006,120(1):37-48
We give new examples of self-shrinking and self-expanding Lagrangian solutions to the Mean Curvature Flow (MCF). These are Lagrangian submanifolds in
, which are foliated by (n − 1)-spheres (or more generally by minimal (n − 1)-Legendrian submanifolds of
), and for which the study of the self-similar equation reduces to solving a non-linear Ordinary Differential Equation (ODE). In the self-shrinking case, we get a family of submanifolds generalising in some sense the self-shrinking curves found by Abresch and Langer. 相似文献
9.
Alexandre Freire 《偏微分方程通讯》2013,38(2):302-327
We consider a system of three surfaces, graphs over a bounded domain in ?2, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to 2π/3.) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic Hölder spaces), for sufficiently regular initial data satisfying a compatibility condition. 相似文献
10.
给出常均曲率热流的Dirichlet边值问题存在唯一和正则的解,并且这个解可以一直达到某个能量集中的时刻.如果这个解还满足一定的能量不等式,那么可以得到在除有限个奇点的全局解.我们所使用的方法有别于文献[2]. 相似文献
11.
本文利用[5]的方法,对R4(C)中平均曲率方向平行的Bonnet曲面引入了半测地等温 参数,并给出了一个分类结果. 相似文献
12.
We prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow and the Poisson bracket deforms due to addition of the Fubini–Study form to the standard symplectic form. 相似文献
13.
In this paper,the authors consider a family of smooth immersions Ft : Mn→Nn+1of closed hypersurfaces in Riemannian manifold Nn+1with bounded geometry,moving by the Hkmean curvature flow.The authors show that if the second fundamental form stays bounded from below,then the Hkmean curvature flow solution with finite total mean curvature on a finite time interval [0,Tmax)can be extended over Tmax.This result generalizes the extension theorems in the paper of Li(see "On an extension of the Hkmean curvature flow,Sci.China Math.,55,2012,99–118"). 相似文献
14.
Shiyu CAO 《数学年刊B辑(英文版)》2023,44(1):1-16
In this paper, the author discusses the deformations of compact complex manifolds with ample canonical bundles. It is known that a complex manifold has unobstructed deformations when it has a trivial canonical bundle or an ample anti-canonical bundle.When the complex manifold has an ample canonical bundle, the author can prove that this manifold also has unobstructed deformations under an extra condition. 相似文献
15.
Lucian Badescu 《Proceedings of the American Mathematical Society》2008,136(5):1505-1513
Let be a submanifold of dimension of the complex projective space . We prove results of the following type.i) If is irregular and , then the normal bundle is indecomposable. ii) If is irregular, and , then is not the direct sum of two vector bundles of rank . iii) If , and is decomposable, then the natural restriction map is an isomorphism (and, in particular, if is embedded Segre in , then is indecomposable). iv) Let and , and assume that is a direct sum of line bundles; if assume furthermore that is simply connected and is not divisible in . Then is a complete intersection. These results follow from Theorem 2.1 below together with Le Potier's vanishing theorem. The last statement also uses a criterion of Faltings for complete intersection. In the case when this fact was proved by M. Schneider in 1990 in a completely different way.
16.
In this paper, we prove the existence and uniqueness of a “steady” spiral moving with forced mean curvature motion. This spiral has a stationary shape and rotates with constant angular velocity. Under appropriate conditions on the initial data, we also show the long time convergence (up to some subsequence in time) of the solution of the Cauchy problem to the steady state. This result is based on a new Liouville result which is of independent interest. 相似文献
17.
Kenro Furutani 《Annals of Global Analysis and Geometry》2002,22(1):1-27
We study a problem of the geometric quantization for the quaternionprojective space. First we explain a Kähler structure on the punctured cotangent bundleof the quaternion projective space, whose Kähler form coincides withthe natural symplectic form on the cotangent bundle and show thatthe canonical line bundle of this complex structure is holomorphicallytrivial by explicitly constructing a nowhere vanishing holomorphicglobal section. Then we construct a Hilbert space consisting of acertain class of holomorphic functions on the punctured cotangentbundle by the method ofpairing polarization and incidentally we construct an operatorfrom this Hilbert space to the L
2 space of the quaternionprojective space. Also we construct a similar operator between thesetwo Hilbert spaces through the Hopf fiberation.We prove that these operators quantizethe geodesic flow of the quaternion projective space tothe one parameter group of the unitary Fourier integral operatorsgenerated by the square root of the Laplacian plus suitable constant.Finally we remark that the Hilbert space above has the reproducing kernel. 相似文献
18.
G 《Differential Geometry and its Applications》2004,20(3):237-277
In this paper, we classify all nonsingular holomorphic spheres in complex Grassmann manifolds G2,5 with the induced constant curvatures K=4, 2, 4/3,1 and 4/5 into some classes, up to unitary equivalence, in which none of the spheres are congruent; At the same time we also prove that there does not exist the nonsingular holomorphic sphere in G2,5 with constant curvature 2/3. 相似文献
19.
Zhang (2021), Luo and Yin (2022) initiated the study of Lagrangian submanifolds satisfying ?*T = 0 or ?*?*T = 0 in Cn or CPn, where T = ?*h and h is the Lagrangian trace-free second fundamental form. They proved several rigidity theorems for Lagrangian surfaces satisfying ?*T = 0 or ?*?*T = 0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2. In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n ≥ 3 and to Lagrangian submanifolds in CPn. 相似文献
20.
基础R0-代数的性质及在L*系统中的应用 总被引:5,自引:1,他引:4
研究了王国俊教授建立的模糊命题演算的形式演绎系统L*和与之在语义上相关的R0-代数,提出了基础R0-代数的观点并讨论了其中的一些性质,在将L*系统中的推演证明转化为相应的R0-代数中的代数运算方面作了一些尝试,作为它的一个应用,证明了L*系统中的模糊演绎定理。 相似文献