S. K. Donaldson
The paper develops various estimates for solutions of a fourth order nonlinear PDE, which corresponds to prescribing the scalar curvature of a toric Kahler metric.
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
We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.
In this paper we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the $C^0$ estimate.
We study a generalized Abreu Equation in $n$-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform $K$-stability.
We study a generalized Abreu equation and derive some estimates.
This paper consists of real and complex affine techniques for studying the Abreu equation on toric surfaces. In particular, an interior estimate for Ricci tensor is given.
A priori interior estimates for special Lagrangian curvature equations
本文针对特殊拉格朗日曲率方程，在临界相和凸情形下建立了先验内部曲率估计，并证明了任意常数相的先验内部梯度估计。
We prove interior gradient estimate and second order estimate for the $Q_k$-flow and $Q_k$-translators in $\mathbb{R}^{n+1}$. In addition, we show that $Q_k$-translator which are asymptotic to $o(|x|)$ cannot exist.
Sharp Interior Gradient Estimate for Area Decreasing Graphical Mean Curvature Flow in Arbitrary Codimension
本文在任意余维情形下证明了面积递减图形式平均曲率流的锐利内部梯度估计，推广了已有结果。
Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
该研究解决了长期问题，证明了所有维度n≥3的常数图形标量曲率方程容许解的内部曲率估计，其证明结合雅可比不等式、双曲面最大值原理与双曲面波戈列洛夫估计。
Interior curvature estimate for curvature quotient equations on convex hypersurfaces
本文针对满足σₙ/σₙ₋₂(λ)=f(X)>0的凸图，研究其曲率商方程的内部曲率估计问题
We establish interior $C^2$ estimates for convex solutions of scalar curvature equation and $σ_2$-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces $(M^n,g)\subset \mathbb R^{n+1}$ with positive scalar curvature. These estimates are consequences of an interior estimate for these equations obtained under a weakened condition.
Interior Hessian estimates for Sigma-2 equations in dimension three
本文在三维空间中证明了 σ_2 = f 的先验内部 C2 估计，推广了 Warren-Yuan 的经典结果。
In this paper we consider the evolution of a graph-like hypersurface by anisotropic mean curvature flow, under some restrictions on the anisotropic area integrand. We find interior estimates (in both time and space) on the gradient of such hypersurfaces, depending only on the height of the graph and the anisotropic area integrand.
Interior estimates and regularity for the scalar curvature equation in dimension 4
该研究针对四维标量曲率方程，采用Shankar和Yuan[SY25]的加倍法，结合小梯度假设的先验加倍不等式与新迭代旋转论证，建立了内部曲率估计及C¹粘性解的内部正则性。
Pogorelov type interior $C^2$ estimate for sum Hessian quotient equations on Riemannian manifolds
针对黎曼流形上一类和Hessian商方程，建立了测地球中心处的内部$C^2$估计以及带零Dirichlet边界的Pogorelov型估计。
A note on interior curvature estimates for strictly convex solutions to the equation of prescribed curvature quotient
本文针对椭圆型Weingarten曲率商方程的严格凸解，借助方程算子的凹性不等式与新颖辅助函数，通过初等最大值原理证明其先验内部曲率界，还得到低维特殊拉格朗日曲率方程严格凸解的对应估计。
Interior curvature estimates for hypersurfaces of prescribing scalar curvature in dimension three
本文通过积分方法，证明了三维空间中预定数量曲率方程超曲面的内部曲率估计，关键发现是满足该方程的图函数对应的拉格朗日子流形具有有界平均曲率。
We extend the interior gradient estimate due to N. Korevaar and L. Simon for solutions of the mean curvature equation from the case of Euclidean graphs to the general case of Killing graphs. Our main application is the proof of existence of Killing graphs with prescribed mean curvature function for continuous boundary data, thus extending a result due to Dajczer, Hinojosa and Lira. In addition, we prove the existence and uniqueness of radial graphs in hyperbolic space with prescribed mean curvature function and asymptotic boundary data at infinity.
Boundary Estimates for the Monge-Ampère Equation in the Polygons with Guillemin Boundary Conditions
研究二维奇异蒙日 - 安培方程在凸多面体上的边界正则性，结合唐纳森的技术及精细论证，将鲁宾和黄的工作扩展到右侧仅赫尔德连续的情况，得到边界上的欧几里得\(C^{1,\alpha/2}\)及\(C^{1,\alpha}\)正则性。
Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t < T.
Pogorelov interior estimates for sum-of-Hessians equations
本文利用Hessian算子求和的凹性，在动态半凸性假设下推导Pogorelov估计，并获得若干Liouville型结果。当k=n-1和k=n时，在可允许锥中建立Pogorelov估计，应用时证明任何在$\mathbb{R}^n$中具有二次增长的整个可允许解必为二次多项式。
In this paper, we consider the Dirichlet problem of a complex Monge-Ampère equation on a ball in $\mathbb C^n$. With $\mathcal C^{1,α}$ (resp. $\mathcal C^{0,α}$) data, we prove an interior $\mathcal C^{1,α}$ (resp. $\mathcal C^{0,α}$) estimate for the solution. These estimates are generalized versions of the Bedford-Taylor interior $\mathcal C^{1,1}$ estimate.
We obtain local pointwise second derivative estimates for $W^{2,p}$-strong solutions to a class of fully nonlinear elliptic equations on Euclidean domains, motivated by problems in conformal geometry.
A delayed interior area-to-height estimate for the Curve Shortening Flow
本文在图形设定下推广了Sobnack与Topping(2024)的结果，证明了曲线缩短流的内部图形估计，并应用该估计证明了从Radon测度弱起始的图形曲线缩短流的存在性。
In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^{2}$. Combined with the a priori interior Hessian estimates proved in [Bha21, Bha22], this solves the Dirichlet boundary value problem for the critical and supercritical Lagrangian mean curvature equation with $C^0$ boundary data. We also provide a uniform gradient estimate for lower regularity phases that satisfy certain additional hypotheses.
We give a maximum principle proof of interior derivative estimates for the Kähler-Ricci flow, assuming local uniform bounds on the metric.
Assume that $M$ is a compact Riemannian manifold of bounded geometry given by restrictions on its diameter, Ricci curvature and injectivity radius. Assume we are given, with some error, the first eigenvalues of the Laplacian $Δ_g$ on $M$ as well as the corresponding eigenfunctions restricted on an open set in $M$. We then construct a stable approximation to the manifold $(M,g)$. Namely, we construct a metric space and a Riemannian manifold which differ, in a proper sense, just a little from $M$ when the above data are given with a small error. We give an explicit $\log\log$-type stability esti…
We derive a priori interior Hessian estimates for the special Lagrangian equation $σ_{2}=1$ in dimension three.
We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two.
We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(κ)=σ\in(0, 1)$ with a prescribed asymptotic boundary $Γ$ at infinity has at least one smooth solution with uniformly bounded hyperbolic principal curvatures. Moreover if $Γ$ is (Euclidean) starshaped, the solution is unique and also (Euclidean) starshaped while if $Γ$ is mean convex the solution is unique. We also show via a strong duality theorem that analogous results hold in De Sitter space. A novel feature…
Linear Poisson Equations with Potential on Riemann Surfaces
本文在满足等周不等式的黎曼曲面上，针对位势项属于 Zygmund 空间的线性泊松方程建立内部估计，并由此得到 Harnack 不等式与全局估计。
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。