Geodesic
Isoperimetric inequalities & volume comparison theorems on CR manifolds
Chanillo, Sagun1  ; Yang, Paul2
1 Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854
2 Department of Mathematics, Princeton University, Princeton, NJ 08544
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 279-307

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In this article we study the Jacobi equation associated with the geodesics in a pseudo-hermitian manifold wish vanishing Webster torsion. We develop integral geometric formula generalizing the well known Santalo formula in Riemannian geometry. As applications we obtain volume comparison results under suitable curvature assumptions as well as isoperimetric inequalities for domains in such manifolds.

Classification : 32V20, 32V05, 53C17, 53C21

Chanillo, Sagun 1 ; Yang, Paul 2

1 Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854
2 Department of Mathematics, Princeton University, Princeton, NJ 08544 
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     title = {Isoperimetric inequalities & volume comparison theorems on {CR} manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {2},
     year = {2009},
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Chanillo, Sagun; Yang, Paul. Isoperimetric inequalities & volume comparison theorems on CR manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 279-307. http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_2_279_0/