-valued differential forms on
Analysis in complex quaternions and its connections with mathematical physics
Residues for monogenic forms on Riemannian manifolds
The paper extends the theory of residues on monogenic forms on domains in (monogenic forms are generalizations of holomorphic forms to Clifford analysis) to monogenic forms on orientable Riemann manifolds.
On generalized Cauchy-Riemann equations on manifolds
Hasse diagrams for parabolic geometries
The invariant differential operators on a manifold with a given parabolic structure come in two classes, standard and non-standard, and can be further subdivided into regular and singular ones. The standard regular operators come in repeated patterns, the Bernstein-Gelfand-Gelfand sequences, described by Hasse diagrams. In this paper, the authors present an alternative characterization of Hasse diagrams, which is quite efficient in the case of low gradings. Several examples are given.
Eigenvalues of conformally invariant operators on spheres
Curved Casimir operators and the BGG machinery.
The nonexistence of a weak solution of Dirichlet's problem for the functional of minimal surface on nonconvex domains
The minimum existence of functional
On the spectrum of a nonlinear operator
Morse-Sard theorem for real-analytic functions
Singular BGG sequences for the even orthogonal case
Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.
O 19. a 20. Hilbertově problému
Integral transforms for divisors in and solutions of systems of PDE’s
On a new normalization for tractor covariant derivatives
A regular normal parabolic geometry of type on a manifold gives rise to sequences of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative on the corresponding tractor bundle , where is the normal Cartan connection. The first operator in the sequence is overdetermined and it is well known that yields the prolongation of this operator in the homogeneous case . Our first main result...
Strengthening upper bound for the number of critical levels of nonlinear functionals
Fischer decompositions in Euclidean and Hermitean Clifford analysis
Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure on Euclidean space and a corresponding second Dirac operator , leading to the system of equations expressing so-called Hermitean monogenicity. The invariance of this...
Morse-Sard theorem in infinite dimensional Banach spaces and investigation of the set of all critical levels
Upper bound for the number of eigenvalues for nonlinear operators (Preliminary communication)
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