Comparison theorems on convex hypersurfaces in Hadamard manifolds

被引：17
作者：
Borisenko, AA
Miquel, V
机构：
[1] Kharkov Natl Univ, Geometry Dept, Math Mech Fac, UA-61007 Kharkov, Ukraine
[2] Univ Valencia, Dept Geometria & Topol, E-46100 Valencia, Spain
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2002年 / 21卷 / 02期
关键词：
circumradius; convex domain; Hadamard manifold; hyperbolic space; inradius; k-th curvature;
D O I：
10.1023/A:1014775603532
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a Hadamard manifold with sectional curvature bounded from below by -k(2)(2), we give sharp upper estimates for the difference circumradius minus inradius of a compact k(2)-convex domain, and we get also estimates for the quotient (Total d-mean curvature)/Area of a convex domain.
引用
收藏
页码：191 / 202
页数：12
相关论文
共 15 条
[1]   LOCALLY CONVEX HYPERSURFACES OF NEGATIVELY CURVED SPACES [J].
ALEXANDER, S .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 64 (02) :321-325
[2]  
Alexander SB., 1993, Proc. Symp. Pure Math, V54, P37, DOI [DOI 10.1090/PSPUM/054.3/1216609, DOI 10.1090/pspum/054.3/1216609]
[3]  
[Anonymous], 1970, J DIFFERENTIAL GEOM
[4]  
[Anonymous], WEAKLY DIFFERENTIABL
[5]  
Borisenko A. A., 1999, MAT FIZ ANAL GEOM, V6, P223
[6]   On locally convex hypersurfaces in Hadamard manifolds [J].
Borisenko, AA .
MATHEMATICAL NOTES, 2000, 67 (3-4) :425-432
[7]   Total curvatures of convex hypersurfaces in hyperbolic space [J].
Borisenko, AA ;
Miquel, V .
ILLINOIS JOURNAL OF MATHEMATICS, 1999, 43 (01) :61-78
[8]   Relation between area and volume for λ-convex sets in Hadamard manifolds [J].
Borisenko, AA ;
Gallego, E ;
Reventós, A .
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2001, 14 (03) :267-280
[9]  
Gray A., 1990, TUBES
[10]   Two problems on h-convex sets in the hyperbolic space [J].
Naveira, AM ;
Tarrio, A .
ARCHIV DER MATHEMATIK, 1997, 68 (06) :514-519
12