In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is...In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is （r, R）-pinched with R/r〈 √2, then there exist at least n -k geometrically distinct P-symmetric closed ∑ characteristics on ∑, as a consequence, Z carry at least n geometrically distinct P-invariant closed characteristics.展开更多
基金supported by China Postdoctoral Science Foundation(Grant No.2013M540512)National Natural Science Foundation of China(Grant Nos.10801078,11171341 and 11271200)Lab of Pure Mathematics and Combinatorics of Nankai University
文摘In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is （r, R）-pinched with R/r〈 √2, then there exist at least n -k geometrically distinct P-symmetric closed ∑ characteristics on ∑, as a consequence, Z carry at least n geometrically distinct P-invariant closed characteristics.
