We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced ...We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced by the authors.展开更多
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.
A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asym...A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.展开更多
基金support from NRFsupported by an NSF granta DARPA grant
文摘We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced by the authors.
基金supported by NSF (Grant No. DMS-0600206)supported by the Korea Science Engineering Foundation (KOSEF) Grant funded by the Korea government (MEST) (No. R01-2008-000-20010-0)supported by the Grant-in-Aid for Scientific Research (B) 18340027
文摘In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.
基金supported by National Research Foundation of Korea(No.2012-011755)a stipend from the Humboldt foundation
文摘A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.
