共查询到20条相似文献,搜索用时 78 毫秒
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在空间形式中, 我们构造了一类泛函, 其临界点包括极小与r 极小超曲面. 给出了临界超曲面的代数、微分和变分刻画. 我们证明了Simons 类不存在定理: 在单位球面中不存在稳定的临界超曲面. 同时证明了Alexandrov 类存在性定理: 在欧氏空间中球面是唯一的稳定的临界超曲面. 相似文献
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本文主要研究平面卵形线的曲率积分不等式.利用积分几何中凸集的支持函数以及外平行集的性质,得到了Gage等周不等式与曲率的熵不等式的一个积分几何的简化证明;进一步地,我们得到了一个新的关于曲率积分的不等式. 相似文献
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讨论在C*-凸理论下C*-代数A的广义态空间SCn(A)中的Krein-Milman型问题.证明了SCn(A)的任意一个BW-紧的C*-凸子集K都具有一个C*-端点,而且K是其C*-端点的C*-凸包. 相似文献
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任何一个可构成实数都是在Lω1中构成的。本文指出,并不是Lω1前面的每一层都会产生新的实数,并用元数学的方法(或者就是模型的方法)对这样的层作了宏观上的描述。 相似文献
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给出了泛函序列Γ-收敛会导致相应梯度流解收敛的充分条件 ,部分证明了DeGiorgi猜想 . 相似文献
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给定一个子群闭的饱和群系F ,定义群类Fpc ,使得G ∈Fpc 当且仅当对于每个子群X ≤G ,存在G的一个F 次正规子群S ,X≤S并且X在S中F 次反正规 .借助F投射子和F覆盖子群 ,给出了Fpc群的特征 . 相似文献
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Paul Baird Ali Fardoun Rachid Regbaoui 《Calculus of Variations and Partial Differential Equations》2006,27(1):75-104
We formulate an appropriate gradient flow in order to study the evolution of the Q-curvature to a prescribed function on a 4-manifold. For a class of prescribed functions, we show convergence and describe the asymptotic behaviour at infinity. 相似文献
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Yamin Wang 《Mathematische Nachrichten》2023,296(5):2150-2166
Let be a closed Riemann surface. Let ψ, h be two smooth functions on Σ with and . In this paper, using the method of flow due to Castras (Pacific J. Math. 276(2015), no. 2, 321–345) and Sun–Zhu (Calc. Var. Partial Differential Equations 60(2021), no. 1, 26), we prove that the solution of the equation exists under given conditions. This gives a new proof of the main results of Zhu (Nonlinear Anal. 169(2018), 38–58). 相似文献
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Cheikh Birahim Ndiaye 《Mathematische Zeitschrift》2011,269(1-2):83-114
Given a compact four-dimensional smooth Riemannian manifold (M,g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero. Using integral methods, we prove global existence and convergence for the Q-curvature flow to a smooth metric conformal to g of prescribed Q-curvature, zero T-curvature and vanishing mean curvature under conformally invariant assumptions. 相似文献
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Ezequiel R. Barbosa Marcos Montenegro 《Bulletin of the Brazilian Mathematical Society》2008,39(3):427-445
In this work we present some properties satisfied by the second L
2-Riemannian Sobolev best constant along the Ricci flow on compact manifolds of dimensions n ≥ 4. We prove that, along the Ricci flow g(t), the second best constant B
0(2, g(t)) depends continuously on t and blows-up in finite time. In certain cases, the speed of the explosion is, at least, the same one of the curvature operator.
We also show that, on manifolds with positive curvature operator or pointwise 1/4-pinched curvature, one of the situations
holds: B
0(2, g(t)) converges to an explicit constant or extremal functions there exists for t large.
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We consider the approach to blow-up in two-dimensional inviscidflows with stagnation-point similitude, in particular a buoyancy-drivenflow resulting from a horizontally quadratic density variationin a horizontally unbounded slab. The blow-up, which is onlypossible because the flow has infinite energy, proceeds by intensificationof the vorticity and density gradient in a layer adjacent tothe upper boundary, while the remainder of the flow tends towardsirrotationality. The governing Boussinesq flow equations arefirst solved numerically, and the results suggest scalings whichare then used in an asymptotic analysis as 0, where is thetime remaining until blow-up. The structure of the asymptoticsolution, involving exponential orders as well as powers andlogarithms of the small parameter, is suggested by the analysisof a simpler related problem for which an exact solution isavailable. The expansion is uniformly valid across the upperboundary layer and the outer region, but there is a layer adjacentto the lower boundary where the flow remains dependent on theinitial conditions and is undetermined by the asymptotics. 相似文献
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Eadah Ahmad Alzahrani & Mohamed Majdoub 《偏微分方程(英文版)》2021,34(1):42-50
We investigate the $p$-Laplace heat equation $u_t-Delta_p u=ζ(t)f(u)$ in a bounded smooth domain. Using differential-inequality arguments, we prove blow-up results under suitable conditions on $ζ, f$, and the initial datum $u_0$. We also give an upper bound for the blow-up time in each case. 相似文献
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Aequationes mathematicae - 相似文献