A geometric problem and the Hopf Lemma

3 Ju l 2 00 5 A geometric problem and the Hopf Lemma

2 9 Ja n 20 06 A geometric problem and the Hopf Lemma

A classical result of A.D. Alexandrov states that a connected compact smooth n−dimensional manifold without boundary, embedded in Rn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X ,Xn+1), (X ′, X̂n+1) on M , with Xn+1 > X̂n+1, the mean curvature at the first is not g...

6 A geometric problem and the Hopf Lemma . II YanYan

A classical result of A.D. Alexandrov states that a connected compact smooth n−dimensional manifold without boundary, embedded in Rn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X ,Xn+1), (X ′, X̂n+1) on M , with Xn+1 > X̂n+1, the mean curvature at the first is not g...

HOPF BIFURCATION CONTROL WITH PD CONTROLLER

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...

A Hopf lemma for higher order differential inequalities and its applications

Article history: Received 14 September 2012 Available online 5 August 2013 We establish a sequential Hopf lemma for higher order differential inequalities in one variable and give some applications of this result. © 2013 Elsevier Inc. All rights reserved.