Geodesic
Vanishing properties of $f$-minimal hypersurfaces in a~complete smooth metric measure space
Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1612-1622

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $(N^{n+1},g,e^{-f}dv)$ be a complete smooth metric measure space with $M^{n}$ being a complete noncompact $f$-minimal hypersurface in $N^{n+1}$. In this paper, we extend the classical vanishing theorems for $L^2$-harmonic $1$-forms on a complete minimal hypersurface to a weighted manifold. In addition, we obtain a vanishing result under the assumption that $M^n$ has sufficiently small weighted $L^n$-norm of the second fundamental form on $M^{n}$, which can be regarded as a generalization of a result by Yun and Seo. Bibliography: 26 titles. 
@article{SM_2020_211_11_a5,
     author = {R. Mi},
     title = {Vanishing properties of $f$-minimal hypersurfaces in a~complete smooth metric measure space},
     journal = {Sbornik. Mathematics},
     pages = {1612--1622},
     publisher = {mathdoc},
     volume = {211},
     number = {11},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_11_a5/}
}
TY  - JOUR
AU  - R. Mi
TI  - Vanishing properties of $f$-minimal hypersurfaces in a~complete smooth metric measure space
JO  - Sbornik. Mathematics
PY  - 2020
SP  - 1612
EP  - 1622
VL  - 211
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2020_211_11_a5/
LA  - en
ID  - SM_2020_211_11_a5
ER  - 
%0 Journal Article
%A R. Mi
%T Vanishing properties of $f$-minimal hypersurfaces in a~complete smooth metric measure space
%J Sbornik. Mathematics
%D 2020
%P 1612-1622
%V 211
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2020_211_11_a5/
%G en
%F SM_2020_211_11_a5
R. Mi. Vanishing properties of $f$-minimal hypersurfaces in a~complete smooth metric measure space. Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1612-1622. http://geodesic.mathdoc.fr/item/SM_2020_211_11_a5/