We will solve an open problem proposed by L.R. Goldberg in ref. [1] (open problem4), and will construct a Teichmuller differential for which there exists a degeneratingHamilton sequence.
In this note,a positive answer for a question posed by S.Bates in 1992 is given,i.e.there exists a C∞ rank=1 map f:l2→R1 such that f(A) has nonempty interior for some subset Al2 of critical points with finite Hausdo...In this note,a positive answer for a question posed by S.Bates in 1992 is given,i.e.there exists a C∞ rank=1 map f:l2→R1 such that f(A) has nonempty interior for some subset Al2 of critical points with finite Hausdorff dimension.It is to say the Morse criticality theorem can not be generalized to infinite-dimensional spaces.展开更多
文摘We will solve an open problem proposed by L.R. Goldberg in ref. [1] (open problem4), and will construct a Teichmuller differential for which there exists a degeneratingHamilton sequence.
文摘In this note,a positive answer for a question posed by S.Bates in 1992 is given,i.e.there exists a C∞ rank=1 map f:l2→R1 such that f(A) has nonempty interior for some subset Al2 of critical points with finite Hausdorff dimension.It is to say the Morse criticality theorem can not be generalized to infinite-dimensional spaces.
