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Sub-elliptic operators
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In this paper we extend the results obtained in [9], [10] to manifolds with SpinC -structures defined, near the boundary, by an almost complex structure. We show that on such a manifold with a strictly pseudoconvex boundary, there ¯ are modified ∂-Neumann boundary conditions defined by projection operators, Reo , which give subelliptic Fredholm problems for the SpinC -Dirac operator, + .eo . We introduce a generalization of Fredholm pairs to the “tame” category.
68p
dontetvui
17-01-2013
64
8
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We assume that the manifold with boundary, X, has a SpinC -structure with spinor bundle S Along the boundary, this structure agrees with the /. structure defined by an infinite order, integrable, almost complex structure and the metric is K¨hler. In this case the SpinC -Dirac operator . agrees with a ¯ ¯ ∂ + ∂ ∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudoconvex or strictly pseudoconcave. We assume that E → X is a complex vector bundle, which has an infinite order, integrable, complex structure along bX, compatible with that defined...
56p
noel_noel
17-01-2013
44
6
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Let X be a compact K¨hler manifold with strictly pseudoconvex bounda ary, Y. In this setting, the SpinC Dirac operator is canonically identified with ¯ ¯ ∂ + ∂ ∗ : C ∞ (X; Λ0,e ) → C ∞ (X; Λ0,o ). We consider modifications of the classi¯ cal ∂-Neumann conditions that define Fredholm problems for the SpinC Dirac operator. In Part 2, [7], we use boundary layer methods to obtain subelliptic estimates for these boundary value problems. Using these results, we obtain an expression for the finite part of the holomorphic Euler characteristic of a strictly pseudoconvex manifold...
33p
noel_noel
17-01-2013
42
5
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Dedicated to Yum-Tong Siu for his 60th birthday. Abstract Let {X1 , . . . , Xp } be complex-valued vector fields in Rn and assume that they satisfy the bracket condition (i.e. that their Lie algebra spans all vector fields). Our object is to study the operator E = Xi∗ Xi , where Xi∗ is the L2 adjoint of Xi . A result of H¨rmander is that when the Xi are real then E is o hypoelliptic and furthemore it is subelliptic (the restriction of a destribution u to an open set U is “smoother” then the restriction...
45p
noel_noel
17-01-2013
46
7
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