Cohomology vanishing theorems for free boundary submanifolds

Vanishing theorems for associative submanifolds

Let M7 a manifold with holonomy in G2, and Y 3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that MX,Y , the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner’s technique, we give a vanishing theorem that forces MX,Y to be locally smooth. MSC 2000: 53C38 (35J55, 53C21, 58J32).

Vanishing Theorems for Coherent Automorphic Cohomology

We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties (such as Shimura varieties) with coefficients in the canonical and subcanonical extensions of automorphic vector bundles, and give explicit conditions for them to vanish in certain degrees. We also provide algorithms for determining all such degrees in practice.

Vanishing theorems for Dolbeault cohomology of log homogeneous varieties

We consider a complete nonsingular variety X over C, having a normal crossing divisor D such that the associated logarithmic tangent bundle is generated by its global sections. We show that H (

F Ur Mathematik in Den Naturwissenschaften Leipzig Vanishing Theorems for L 2 -cohomology Groups Vanishing Theorems for L 2 -cohomology Groups

Cohomology of CR-submanifolds

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