Geodesic
Semigroup properties for the second fundamental form
Documenta mathematica, Tome 15 (2010), pp. 527-543
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Let M be a compact Riemannian manifold with boundary ∂M and L=δ+Z for a C1-vector field Z on M. Several equivalent statements, including the gradient and Poincaré/log-Sobolev type inequalities of the Neumann semigroup generated by L, are presented for lower bound conditions on the curvature of L and the second fundamental form of ∂M. The main result not only generalizes the corresponding known ones on manifolds without boundary, but also clarifies the role of the second fundamental form in the analysis of the Neumann semigroup. Moreover, the Lévy-Gromov isoperimetric inequality is also studied on manifolds with boundary.
DOI : 10.4171/dm/305
Classification : 60J60
Mots-clés : Poincaré inequality, second fundamental form, gradient estimate, Neumann semigroup, log-Sobolev inequality 
@article{10_4171_dm_305,
     author = {Feng-Yu Wang},
     title = {Semigroup properties for the second fundamental form},
     journal = {Documenta mathematica},
     pages = {527--543},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/305},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/305/}
}
TY  - JOUR
AU  - Feng-Yu Wang
TI  - Semigroup properties for the second fundamental form
JO  - Documenta mathematica
PY  - 2010
SP  - 527
EP  - 543
VL  - 15
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/305/
DO  - 10.4171/dm/305
ID  - 10_4171_dm_305
ER  - 
%0 Journal Article
%A Feng-Yu Wang
%T Semigroup properties for the second fundamental form
%J Documenta mathematica
%D 2010
%P 527-543
%V 15
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/305/
%R 10.4171/dm/305
%F 10_4171_dm_305
Feng-Yu Wang. Semigroup properties for the second fundamental form. Documenta mathematica, Tome 15 (2010), pp. 527-543. doi: 10.4171/dm/305

Cité par Sources :