Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.

基于曲率驱动的p-harmonic模型图像修复算法

在p-harmonic模型的基础上,引入曲率诱导项,提出一种新的图像修复模型,建立了与之对应的扩散方程,利用有限差分法对所建立的扩散方程进行数值求解,给出该修补模型的离散格式和具体的算法步骤,得到修复的图像。实验结果表明:该算法能提高修复的速度,并且具有较好的修补效果。

Some results on P-harmonic maps and exponentially harmonic maps between Finsler manifolds

This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li＇s results in [2] and [3].

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.

The Concavity of the Gaussian Curvature of the Convex Level Sets of p-Harmonic Functions with Respect to the Height

For the p-harmonic function with strictly convex level sets,we find an auxiliary function which comes from the combination of the norm of gradient of the p-harmonic function and the Gaussian curvature of the level sets of p-harmonic function.We prove that this curvature function is concave with respect to the height of the p-harmonic function.This auxiliary function is an affine function of the height when the p-harmonic function is the p-Green function on ball.

The method of p-harmonic approximation and optimal interior partial regularity for energy minimizing p-harmonic maps under the controllable growth condition

In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.

Regularity for P-Harmonic Type Systems with the Gradients below the Controllable Growth

In this paper, we shall establish that each weak solution of p-harmonic type systems with the gradients below the controllable growth belongs to, Holder continuity spaces with any HSlder exponent α∈ [0, 1）. Furthermore, we can obtain that the gradients of the corresponding weak solutions also belong to locally Hoelder continuity spaces with some Hoelder exponent. Keywords controllable growth, p-harmonic systems, full regularity MR（2000） Subject Classification 35J60, 35B65

The p-Harmonic Heat Flow with Potential into Homogeneous Spaces

Abstract l11 tl1is papel' xte I7rove tl1e existellce of gIol>al wcak so1utiolls of the I)--11i1r11loliic flow with potelltial bett'eel1 Rit)mal1nian lnallifOlds AI an(l N fbr arbitrary iuitial data 1la\-i11g fl11ite P--e11erg}: ill the case wI1e11 the targct N is a l1on1ogeneous spact. witll a left invariant ln(3tri<'.

Liouville Type Theorem About p-Harmonic Function and p-Harmonic Map with Finite L^q-Energy

This paper deals with the p-harmonic function on a complete non-compact submanifold M isometrically immersed in an(n + k)-dimensional complete Riemannian manifold M of non-negative(n-1)-th Ricci curvature. The Liouville type theorem about the p-harmonic map with finite L^q-energy from complete submanifold in a partially nonnegatively curved manifold to non-positively curved manifold is also obtained.

On the Construction of p-Harmonic Morphisms and Conformal Actions

We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.

Augmented Lagrangian Methods for p-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

In this paper,we propose a generalized penalization technique and a convex constraint minimization approach for the p-harmonic flow problem following the ideas in[Kang&March,IEEE T.Image Process.,16(2007),2251–2261].We use fast algorithms to solve the subproblems,such as the dual projection methods,primal-dual methods and augmented Lagrangian methods.With a special penalization term,some special algorithms are presented.Numerical experiments are given to demonstrate the performance of the proposed methods.We successfully show that our algorithms are effective and efficient due to two reasons:the solver for subproblem is fast in essence and there is no need to solve the subproblem accurately(even 2 inner iterations of the subproblem are enough).It is also observed that better PSNR values are produced using the new algorithms.

f-Harmonic Morphisms Between Riemannian Manifolds

f-Harmonic maps were first introduced and studied by Lichnerowicz in 1970.In this paper,the author studies a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions.The author proves that a map between Riemannian manifolds is an f-harmonic morphism if and only if it is a horizontally weakly conformal f-harmonic map.This generalizes the well-known characterization for harmonic morphisms.Some properties and many examples as well as some non-existence of f-harmonic morphisms are given.The author also studies the f-harmonicity of conformal immersions.