Solvable Lie Algebras and Generalized Cartan Matrices Arising from Isolated Singularities.
Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
Let and be two compact strongly pseudoconvex CR manifolds of dimension which bound complex varieties and with only isolated normal singularities in and respectively. Let and be the singular sets of and respectively and is nonempty. If and the cardinality of is less than 2 times the cardinality of , then we prove that any non-constant CR morphism from to is necessarily a CR biholomorphism. On the other hand, let be a compact strongly pseudoconvex CR manifold of...
Variation of complex structures and variation of Lie algebras.
Equivalences between isolated hypersurface singularities.
An obstruction for smoothing of Gorenstein surface singularities.
Diffeomorphic types of the complements of arrangements of hyperplanes
Intersection lattices and topological structures of complements of arrangements in
A sharp estimate of the number of integral points in a tetrahedron.
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
Classification of Isolated Hypersurface Singularities by Their Moduli Algebras.
Holomorphic symmetries
An estimate of the gap of the first two eigenvalues in the Schrödinger operator
On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function
It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function which is the number of positive integers and free of prime factors . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional () real right-angled simplices. In this paper, we...
Counterexample to boundary regularity of a strongly pseudoconvex CR submanifold: An addendum to the paper of Harvey-Lawson.
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