25 Result(s)

Chapter and Conference Paper

A Car as Parabolic Geometry

We show that a car, viewed as a nonholonomic system, provides an example of a flat parabolic geometry of type (SO(2, 3), P ₁₂), where P ₁₂ is a Borel parabolic subgroup in SO(2, 3). We discuss the relations of th...

C. Denson Hill, Paweł Nurowski in Geometry, Lie Theory and Applications (2022)

Article

Aspects of the Levi form

We discuss various analytical and geometrical aspects of the Levi form, which is associated with a CR manifold having any CR dimension and any CR codimension.

Judith Brinkschulte, C. Denson Hill… in Bollettino dell'Unione Matematica Italiana (2020)

Article

Lorentzian CR structures and nonembeddability

In this paper we construct examples of CR deformations of Lorentzian hypersurfaces which are CR embeddable at all points outside an arbitrarily small compact set whose interior contains a point where CR embeddabl...

Judith Brinkschulte, C. Denson Hill in manuscripta mathematica (2018)

Article

Inflexible CR submanifolds

In this paper we introduce the concept of inflexible CR submanifolds. These are CR submanifolds of some complex Euclidean space such that any compactly supported CR deformation is again g...

Judith Brinkschulte, C. Denson Hill in Mathematische Zeitschrift (2017)

Article

On the nonvanishing of abstract Cauchy–Riemann cohomology groups

In this paper we prove infinite dimensionality of some local and global cohomology groups on abstract Cauchy–Riemann manifolds.

Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich in Mathematische Annalen (2016)

Article

Malgrange’s vanishing theorem for weakly pseudoconcave C R manifolds

We prove the Malgrange vanishing and approximation theorems for smooth, abstract, weakly pseudoconcave C R manifolds of finite kind.

Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich in manuscripta mathematica (2010)

Article

On the Cauchy problem for the \(\bar\partial\) operator

We present new results concerning the solvability, or lack of thereof, in the Cauchy problem for the \(\bar\partial\) o...

Judith Brinkschulte, C. Denson Hill in Arkiv för Matematik (2009)

Article

On the failure of the Poincaré Lemma for II

C. Denson Hill, Mauro Nacinovich in Mathematische Annalen (2006)

Article

Integrability of rough almost complex structures

We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz regularity. We also discuss the regularity of local holomorphic coordinates in the i...

C. Denson Hill, Michael Taylor in The Journal of Geometric Analysis (2003)

Article

On the failure of the Poincaré lemma for the \({\bar\partial_M}\) complex

C. Denson Hill, Mauro Nacinovich in Mathematische Annalen (2002)

Article

A weak pseudoconcavity condition for abstract almost CR manifolds

C. Denson Hill, Mauro Nacinovich in Inventiones mathematicae (2000)

Article

Conormal suspensions of differential complexes

C. Denson Hill, Mauro Nacinovich in The Journal of Geometric Analysis (2000)

Article

Spinning analytic discs and domains of dependence

In this paper we introduce a new technique of spinning analytic discs, which allows us to control the direction of CR extension of CR functions from rigid CR manifolds.

Roman Dwilewicz, C. Denson Hill in manuscripta mathematica (1998)

Article

Aneurysms of pseudoconcaveCR manifolds

C. Denson Hill, Mauro Nacinovich in Mathematische Zeitschrift (1995)

Chapter

Effective Computation of the Symmetric Lens

We present an effective numerical scheme to compute, to any desired degree of accuracy, the shape of a symmetric lens of unit radius with given index of refraction and prescribed foci on the axis of symmetry. ...

C. Denson Hill, Perry Susskind, Vincent Giambalvo in Applied and Industrial Mathematics (1991)