This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.
In this short note,we give a proof of our partial C^0-estimate for Kähler-Einstein metrics.Our proof uses a compactness theorem of Cheeger-Colding-Tian and L^2-estimate for∂^--operator.
We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimat...We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.展开更多
All C*-algebras of sections of locally trivial C*-algebra bundles over ∏si=1 Lki (ni)with fibres Aω Mc(C) are constructed, under the assumption that every completely irra-tional noncommutative torus Aω is realized ...All C*-algebras of sections of locally trivial C*-algebra bundles over ∏si=1 Lki (ni)with fibres Aω Mc(C) are constructed, under the assumption that every completely irra-tional noncommutative torus Aω is realized as an inductive limit of circle algebras, whereLki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over ∏si=1 Lki (ni) × Tr+2whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized asC(Tr) Al/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lcd p is defined by twisting C*(Tr+2) C*(Zm-2)in Lcd C*(Zm-2) by a totally skew multiplier ρ on Tr+2 × Zm-2. It is shown thatLcdp Mp∞ is isomorphic to (∏si=1 Lki (ni)) Aρ Mcd(C) Mp∞ if and only if the setof prime factors of cd is a subset of the set of prime factors of p, and that Lcd p is not stablyisomorphic to C(∏si=1 Lki (ni)) Aρ Mcd(C) if the cd-homogeneous C*-subalgebra ofLcdp restricted to some subspace Lki (ni) ∏si=1 Lki (ni) is realized as the crossed productby the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 forki an integer greater than 1.展开更多
The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)...The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)-estimate was used by Jeffres-MazzeoRubinstein in their proof of the existence of K¨ahler-Einstein metrics with conic singularities.展开更多
基金Both authors are supported by NSF grant DMS9970840 This material is also based uponwork supported by,the U.S. Army Research Office under grant number DAADl9-00-1-0152 for both authors.
文摘This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.
文摘In this short note,we give a proof of our partial C^0-estimate for Kähler-Einstein metrics.Our proof uses a compactness theorem of Cheeger-Colding-Tian and L^2-estimate for∂^--operator.
基金supported by Le Centre de recherche en géométrie et topologie Fellowship during the visit to Institut des sciences mathématiques of Universitédu QuébecàMontréal。
文摘We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.
基金The author was supported by grant No. 1999-2-102-001-3 from the interdis- ciplinary research program year of the KOSEF.
文摘All C*-algebras of sections of locally trivial C*-algebra bundles over ∏si=1 Lki (ni)with fibres Aω Mc(C) are constructed, under the assumption that every completely irra-tional noncommutative torus Aω is realized as an inductive limit of circle algebras, whereLki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over ∏si=1 Lki (ni) × Tr+2whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized asC(Tr) Al/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lcd p is defined by twisting C*(Tr+2) C*(Zm-2)in Lcd C*(Zm-2) by a totally skew multiplier ρ on Tr+2 × Zm-2. It is shown thatLcdp Mp∞ is isomorphic to (∏si=1 Lki (ni)) Aρ Mcd(C) Mp∞ if and only if the setof prime factors of cd is a subset of the set of prime factors of p, and that Lcd p is not stablyisomorphic to C(∏si=1 Lki (ni)) Aρ Mcd(C) if the cd-homogeneous C*-subalgebra ofLcdp restricted to some subspace Lki (ni) ∏si=1 Lki (ni) is realized as the crossed productby the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 forki an integer greater than 1.
文摘The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)-estimate was used by Jeffres-MazzeoRubinstein in their proof of the existence of K¨ahler-Einstein metrics with conic singularities.
