scholarly journals A Morse theoretical approach for the boundary mean curvature problem on B4

2008 ◽  
Vol 254 (5) ◽  
pp. 1307-1341 ◽  
Author(s):  
Wael Abdelhedi ◽  
Hichem Chtioui ◽  
Mohameden Ould Ahmedou
Keyword(s):  
Theoretical Approach ◽  
Mean Curvature ◽  
Curvature Problem ◽  
Boundary Mean Curvature

Topological Methods for Boundary Mean Curvature Problem on Bn

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Mohammed Ali Al-Ghamdi ◽  
Hichem Chtioui ◽  
Khadijah Sharaf
Keyword(s):  
Critical Points ◽  
Mean Curvature ◽  
Topological Method ◽  
Topological Methods ◽  
Critical Points At Infinity ◽  
The Mean ◽  
Curvature Problem ◽  
Boundary Mean Curvature

AbstractUsing an algebraic topological method and the tools of the theory of the critical points at infinity, we provide a variety of classes of functions that can be realized as the mean curvature on the boundary of the the n-dimensional balls.

scholarly journals Existence and Multiplicity Results for the Scalar Curvature Problem on the Half-Sphere 𝕊+3

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ridha Yacoub
Keyword(s):  
Scalar Curvature ◽  
Critical Points ◽  
Mean Curvature ◽  
Existence Results ◽  
Curvature Condition ◽  
Multiplicity Results ◽  
3 Dimensional ◽  
Existence And Multiplicity ◽  
Curvature Problem ◽  
Boundary Mean Curvature

In this paper we deal with the scalar curvature problem under minimal boundary mean curvature condition on the standard 3-dimensional half-sphere. Using tools related to the theory of critical points at infinity, we give existence results under perturbative and nonperturbative hypothesis, and with the help of some “Morse inequalities at infinity”, we provide multiplicity results for our problem.

scholarly journals The prescribed boundary mean curvature problem on B4

2004 ◽  
Vol 206 (2) ◽  
pp. 373-398 ◽  
Author(s):  
Zindine Djadli ◽  
Andrea Malchiodi ◽  
Mohameden Ould Ahmedou
Keyword(s):  
Mean Curvature ◽  
Curvature Problem ◽  
Boundary Mean Curvature

scholarly journals Infinitely Many Solutions for the Prescribed Boundary Mean Curvature Problem in 𝔹N

2013 ◽  
Vol 65 (4) ◽  
pp. 927-960 ◽  
Author(s):  
Liping Wang ◽  
Chunyi Zhao
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
Local Maximum ◽  
Infinitely Many Solutions ◽  
Maximum Point ◽  
Euclidean Metric ◽  
Rotationally Symmetric ◽  
Local Maximum Point ◽  
Curvature Problem ◽  
Boundary Mean Curvature

AbstractWe consider the prescribed boundary mean curvature problem in 𝔹N with the Euclidean metric where ã(x) is positive and rotationally symmetric on We show that if K∽(x) has a local maximum point, then this problemhas infinitely many positive solutions that are not rotationally symmetric on 𝕊N−1.

Positive Solutions of an Indefinite Prescribed Mean Curvature Problem on a General Domain

2004 ◽  
Vol 4 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Patrick Habets ◽  
Pierpaolo Omari
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
General Domain ◽  
Prescribed Mean Curvature ◽  
Existence Of Positive Solutions ◽  
Curvature Problem

AbstractThe existence of positive solutions is proved for the prescribed mean curvature problemwhere Ω ⊂ℝ

scholarly journals The free-boundary Brakke flow

2020 ◽  
Vol 2020 (758) ◽  
pp. 95-137 ◽  
Author(s):  
Nick Edelen
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Monotonicity Formula ◽  
Local Regularity ◽  
Regularity Theorem ◽  
Elliptic Regularization ◽  
Barrier Surface ◽  
Boundary Mean Curvature

AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

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