本文聚焦于四维自对偶与偶Poincaré-Einstein度量，解决了该类度量在存在性与刚性方面的关键问题。研究者通过引入新的三维共形不变量I0，并结合Yamabe不变量，证明了新的刚性定理与间隙定理，揭示了边界共形不变量与流形拓扑之间的深刻联系，为理解该类度量 ...

Were it not for the Poincaré conjecture, it is doubtful whether many non-mathematicians today would know of Henri Poincaré. His vexed question in topology was solved only in 2003 — nearly a century ...

Dr Grigori Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences, St Petersburg, has been touring US universities describing his work in a series of papers not yet ...

Since it was proposed by polymath H. Poincare' in 1904, who sought to mathematically define the topology of a sphere, mathematicians had sought to prove the theorem. For more than a century, the best ...

Hyam Rubinstein receives funding from the Australian Research Council and has also received funding from several mining companies for research on the optimal design of access networks in underground ...

The New York Times recently reported that reclusive Russian geometer Grigory Perelman has apparently proved the century-old Poincaré conjecture. The Times calls Poincaré “a landmark not just of ...

In his classical textbook on mechanics, Edmund Whittaker described the three-body problem as “the most celebrated of all dynamical problems”. From 1906 to 1912, Whittaker was Andrews Professor at ...