Paper Information

Journal:   IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE   FALL 2006 , Volume 30 , Number A3; Page(s) 285 To 289.
 
Paper: 

COMPACT HYPERSURFACES IN EUCLIDEAN SPACE AND SOME INEQUALITIES

 
 
Author(s):  BEKTAS D.*, ERGUT M.
 
* DEPARTMENT OF MATHEMATICS, FIRAT UNIVERSITY, 23119 ELAZIG, TURKEY
 
Abstract: 

Let (M,g) be a compact immersed hypersurface of (Rn+1,<,>), l1 the first nonzero eigenvalue, a the mean curvature, P the support function, A the shape operator, vol(M) the volume of M, and S the scalar curvature of M. In this paper, we established some eigenvalue inequalities and proved the above.
1/n
òM \\A\\2 P2DV ³ </span></p>M  a2 P2 dV.
2
òM a2 P2 dV ³ 1/n (n-1) òM sp2 dV.
If the scalar curvature S and the first nonzero eigenvalue l1 staisfy S= l1 (N-1), than òM [a2 - l1/n] p2 dv³ 0,
4) Suppose that the Ricci curvature of M is bounded below by a positive constant k. Thus
òM a2 P2 dV ³ k/n(n-1) òM \\ gradf\\ dv+vol(M).
5) Suppose that the Ricci curvature is bounded and the scalar curvature satisfy S=
l1(n− 1) and L=k- 2S>0 is a constant. Thus
vol (M)
³ kl1 /L òM\\ Y \\ a pdv – 2S/L òM a2 P2 Dv.

 
Keyword(s): FIRST EIGENVALUE, SUPPORT FUNCTION
 
References: 
  • ندارد
 
  pdf-File tarjomyar Yearly Visit 102
 
Latest on Blog
Enter SID Blog