An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities

Analysis ◽  
2009 ◽  
Vol 29 (2) ◽  
Author(s):  
Stefan Hildebrandt ◽  
Friedrich Sauvigny
Keyword(s):  
Mean Curvature ◽  
Energy Estimate ◽  
Removable Singularities ◽  
Prescribed Mean Curvature ◽  
Dimensional Equation ◽  
The Difference

PRESCRIBING MEAN CURVATURE ON 𝔹n

2010 ◽  
Vol 21 (09) ◽  
pp. 1157-1187 ◽  
Author(s):  
WAEL ABDELHEDI ◽  
HICHEM CHTIOUI
Keyword(s):  
Critical Points ◽  
Mean Curvature ◽  
Level Sets ◽  
Curvature Function ◽  
Number Of Solutions ◽  
Total Contribution ◽  
Prescribed Mean Curvature ◽  
The Difference ◽  
Zero Scalar Curvature ◽  
Lagrange Functional

In this paper, we consider the problem of multiplicity of conformal metrics that are equivalent to the Euclidean metric, with zero scalar curvature and prescribed mean curvature on the boundary of the ball 𝔹n, n ≥ 4. Under the assumption that the order of flatness at critical points of the prescribed mean curvature function H(x) is β∈(n-2, n-1), we establish some Morse inequalities at infinity, which give a lower bound on the number of solutions to the above problem, in terms of the total contribution of its critical points at infinity to the difference of topology between the level sets of the associated Euler–Lagrange functional. As a by-product of our arguments, we derive a new existence result through an Euler–Hopf type formula.

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 Embedded tori with prescribed mean curvature

2018 ◽  
Vol 340 ◽  
pp. 406-458 ◽  
Author(s):  
Paolo Caldiroli ◽  
Monica Musso
Keyword(s):  
Mean Curvature ◽  
Prescribed Mean Curvature
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