Haozhao Li
Using Perelman's results on Kahler Ricci flow, we prove that the K energy is bounded from below if and only if the F functional is bounded from below in the canonical Kahler class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The main result of this paper shows that "test configurations" give new lower bounds on the $L^{2}$ norm of the scalar curvature on a Kahler manifold. This is closely analogous to the analysis of the Yang-Mills functional over Riemann surfaces by Atiyah and Bott. The proof uses asymptotic approximation by finite-dimensional problems: the essential ingredient being the Tian-Zelditch-Lu expansion of the "density of states" function.
We study the energy functional on the set of Lagrangian tori in $\mathbb{C}P^2$ . We prove that the value of the energy functional on a certain family of Hamiltonian minimal Lagrangian tori in $\mathbb{C}P^2$ is strictly larger than energy of the Clifford torus.
For $n$-dimensional weighted Riemannian manifolds, lower $m$-Bakry-Émery-Ricci curvature bounds with $\varepsilon$-range, introduced by Lu-Minguzzi-Ohta, integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower $m$-Bakry-Émery-Ricci curvature bounds with $\varepsilon$-range. These generalize those inequalities under constant curvature bounds for $m \in (n,\infty)$ to $m\in(-\infty,1]\cup\{\infty\}$.
In the present paper, we prove a stability theorem for the Kaehler Ricci flow near the infimum of the functional E_1 under the assumption that the initial metric has Ricci > -1 and |Riem| bounded. At present stage, our main theorem still need a topological assumption (1.2) which we hope to be removed in subsequent papers. The underlying moral is: if a Kaehler metric is sufficiently closed to a Kaehler Einstein metric, then the Kaehler Ricci flow converges to it. The present work should be viewed as a first step in a more ambitious program of deriving the existence of Kaehler Einstein metrics w…
We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in $\mathbb{R}^n$. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity.
Convergence of the area functional on spaces with lower Ricci bounds and applications
本文证明热流在 RCD 空间上逼近面积泛函，建立面积公式与松弛一致性，获得周长最小化函数的正则性与唯一性，并应用于极限空间中的极小元逼近及 Ricci 极限空间。
In this short note we prove that the degree of the Gauss map ν of a closed 3-dimensional hypersurface of the Euclidean space is a lower bound for the total bending functional B, introduced by G. Wiegmink. Consequently, the energy functional E introduced by C. M. Wood admits a topological lower bound.
In this paper, we generalize Chen-Tian energy functionals to Kähler-Ricci solitons and prove that the properness of these functionals is equivalent to the existence of Kähler-Ricci solitons. We also discuss the equivalence of the lower boundedness of these functionals and their relation with Tian-Zhu's holomorphic invariant.
In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with conical initial data. In the second part, we define a geometric invariant lambda_AF for asymptotically flat manifolds with nonnegative scalar curvature. This invariant gives a quantitative lower bound for the ADM-mass from general relativity, motivates a Ricci flow proof of the r…
We will study the blowup behavior of a surface sequence immersed in $R^2$ with bounded Willmore functional and fixed genus.
Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the Gårding inequality for global pseudo-differential operators associated with boundary value problems. The analysis that we follow is free of local coordinate systems. Applications of the Gårding inequality to the global solvability for a class of evolution problems are also considered.
Lower bounds on fibered Yang-Mills functionals: generic nefness and semistability of direct images
本文研究纤维化Yang-Mills函数的下界，通过holomorphic向量丛的Harder-Narasimhan滤子与极化纤维化的关系，探讨直接像sheaves的斜率及通用nef性与半稳定性的联系。
In this paper we provide an explicit formula for the optimal lower bound of Donaldson's J-functional, in the sense of finding explicitly the optimal constant in the definition of coercivity, which always exists and takes negative values in general. This constant is positive precisely if the J-equation admits a solution, and the explicit formula has a number of applications. First, this leads to new existence criteria for constant scalar curvature Kähler (cscK) metrics in terms of Tian's alpha invariant. Moreover, we use the above formula to discuss Calabi dream manifolds and an analogous notio…
For a bounded smooth domain in the plane and smooth boundary data we consider the minimisation of the Willmore functional for graphs subject to Dirichlet or Navier boundary conditions. For $H^2$-regular graphs we show that bounds for the Willmore energy imply area and diameter bounds. We then consider the $L^1$-lower semicontinuous relaxation of the Willmore functional, which is shown to be indeed its largest possible extension, and characterise properties of functions with finite relaxed energy. In particular, we deduce compactness and lower-bound estimates for energy-bounded sequences. The l…
Let $X$ be a compact Kähler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a Kähler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus Donaldson--Futaki invariants of test configurations of $(X,L)$. He also conjectured that the bound is sharp. In this paper, we prove a metric analogue of Donaldson's conjecture, we show that if we enlarge the space of test configurations to the space of geodesic rays in $\mathcal{E}^2$ and replace the Donaldson--Futaki invariant by the radial Mabuchi K-energy $\…
Over the space of Kähler metrics associated to a fixed Kähler class, we first prove the lower bound of the energy functional $\tilde E^β$, then we provide the criterions of the geodesics rays to detect the lower bound of $\tilde {\mathfrak J}^β$-functional. They are used to obtain the properness of Mabuchi's $K$-energy. The criterions are examined by showing the convergence of the negative gradient flow of $\tilde {\mathfrak J}^β$-functional.
We address the minimization of the Canham-Helfrich functional in presence of multiple phases. The problem is inspired by the modelization of heterogeneous biological membranes, which may feature variable bending rigidities and spontaneous curvatures. With respect to previous contributions, no symmetry of the minimizers is here assumed. Correspondingly, the problem is reformulated and solved in the weaker frame of oriented curvature varifolds. We present a lower semicontinuity result and prove existence of single- and multiphase minimizers under area and enclosed-volume constrains. Additionally…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。