Rongli Huang

Guangxi Normal University

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Jiguang Bao

Washington University in St. Louis

Yun‐Hua Ye

Jiangxi Normal University

Chong Wang

Cangzhou Normal University

Qianzhong Ou

Guangxi Normal University

Juanjuan Chen

Macau University of Science and Technology

Zhizhang Wang

Southern Medical University

Wenlong Wang

Zhengzhou University

Sitong Li

China Pharmaceutical University

Carlos José Soares

Universidade Federal de Uberlândia

Zilong Li

Chongqing University

Cooperative Institutions

Sun Yat-sen University

Guangxi Normal University

Chinese Academy of Sciences

Key Laboratory of Guangdong Province

Beijing Normal University

Dalian University of Technology

University of Science and Technology of China

Bureau of Geology and Mineral Exploration and Development of Guizhou Province

Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou)

Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai)

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On the Second Boundary Value Problem for a Class of Fully Nonlinear Flow Iii

Chong Wang Rongli Huang Jiguang Bao

We study the solvability of the second boundary value problem of the Lagrangian mean curvature equation arising from special Lagrangian geometry. By the parabolic method we obtain the existence and uniqueness of the smooth uniformly convex solution, which generalizes the Brendle-Warren's theorem about minimal Lagrangian diffeomorphism in Euclidean metric space.

Value (mathematics)

10.2139/ssrn.4617395

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On the second boundary value problem for a class of fully nonlinear flows II

Archiv der Mathematik (2018)

Juanjuan Chen Rongli Huang Yun‐Hua Ye

Continuation

10.1007/s00013-018-1197-6

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Citations (6)

On the Second Boundary Value Problem for a Class of Fully Nonlinear Flows I

International Mathematics Research Notices (2017)

Rongli Huang Yun‐Hua Ye

Abstract In this article, a class of fully nonlinear flows with nonlinear Neumann type boundary condition is considered. This problem was solved partly by the first author under the assumption that the flow is the parabolic type special Lagrangian equation in $\mathbb{R}^{2n}$. We show that the convexity is preserved for solutions of the fully nonlinear parabolic equations and prove the long time existence and convergence of the flow. In particular, we can prescribe the second boundary value problems for a family of special Lagrangian graphs in Euclidean and pseudo-Euclidean space.

Convexity

10.1093/imrn/rnx278

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On the entire self-shrinking solutions to Lagrangian mean curvature flow II

Calculus of Variations and Partial Differential Equations (2022)

Rongli Huang Qianzhong Ou Wenlong Wang

Rigidity (electromagnetism)

10.1007/s00526-022-02333-1

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Existence and Regularity for Some Degenerate Parabolic Equation

Differential Equations and Dynamical Systems (2019)

Rongli Huang Jiguang Bao

Nabla symbol

Viscosity solution

10.1007/s12591-019-00460-4

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Two Corollaries About The Perron-Frobenius Theorem

Journal of Zhanjiang Teachers College (2004)

Rongli Huang

In this paper, two corollaries and some results are presented according to the Perron-Frobenius Theorem,which reflect the connection of character subspaces of irreducible nonnegative matrices,and the model of the connected eigenvalues equal the spectral radius.This paper improves some results on this topic to some extent.

Spectral Radius

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Dynamics of the Difference Equation x_(n+1)=p_n+x_n/x_(n-1)

Journal of Guangxi Normal University (2013)

Rongli Huang

This paper studies the dynamics of the difference equationxn+1=pn+xn/xn-1,n=0,1,…where the parameter pn is a period-three sequence with initial values x-1,x0∈(0,+∞).Results show that every positive solution of this equation converges to a unique period-three solutions and the difference equation has global asymptotic stability.

Matrix difference equation

Sequence (biology)

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Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space II

arXiv (Cornell University) (2024)

Shanshan Li J.C. Lv Rongli Huang

In this paper, we consider the mean curvature flow of entire Lagrangian graphs with initial data in the pseudo-Euclidean space, which is related to the special Lagrangian parabolic equation. We show that the parabolic equation \eqref{11} has a smooth solution $u(x,t)$ for three corresponding nonlinear equations between the Monge-Amp$\grave{e}$re type equation($\tau=0$) and the special Lagrangian parabolic equation($\tau=\frac{\pi}{2}$). Furthermore, we get the bound of $D^lu$, $l=\{3,4,5,\cdots\}$ for $\tau=\frac{\pi}{4}$ and the decay estimates of the higher order derivatives when $0<\tau<\frac{\pi}{4}$ and $\frac{\pi}{4}<\tau<\frac{\pi}{2}$. We also prove that $u(x,t)$ converges to smooth self-expanding solutions of \eqref{12}.

10.48550/arxiv.2410.17794

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The blow up analysis of the general curve shortening flow

arXiv (Cornell University) (2009)

Rongli Huang Jiguang Bao

It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.

10.48550/arxiv.0908.2036

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On the Second Boundary Value Problem for a Class of Fully Nonlinear Equations

Journal of Geometric Analysis (2017)

Rongli Huang Qianzhong Ou

10.1007/s12220-017-9774-7

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Citations (9)