Divergence theorems and the supersphere

@article{Groeger2013DivergenceTA,
  title={Divergence theorems and the supersphere},
  author={Josua Groeger},
  journal={Journal of Geometry and Physics},
  year={2013},
  volume={77},
  pages={13-29}
}
  • Josua Groeger
  • Published 5 September 2013
  • Mathematics
  • Journal of Geometry and Physics
View PDF on arXiv
22 Citations
Highly Influential Citations
2
Background Citations
4

22 Citations

Non-Euclidean Fourier Inversion on Super-hyperbolic Space

For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason–Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the…

Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces

We compute the Harish-Chandra c-function for a generic class of rank-one purely non-compact Riemannian symmetric super- spaces X = G/K in terms of Euler functions, proving that it is meromorphic.…

Killing Vector Fields and Superharmonic Field Theories

The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high…

Fourier Analysis on Non-Compact Symmetric Superspaces of Rank One

This thesis covers two topics. The first part studies the asymptotic behaviour of spherical super functions on non-compact symmetric super spaces of low rank. This plays an important role in the…

On Complex Supermanifolds with Trivial Canonical Bundle

We give an algebraic characterisation for the triviality of the canonical bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky superalgebra structure. As an application, we…

Dynamics of a Diffusive Multigroup SVIR Model with Nonlinear Incidence

A multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, is investigated and the global stability of the endemic equilibria is established.

Analysis of a general multi-group reaction-diffusion epidemic model with nonlinear incidence and temporary acquired immunity

Bifurcation Analysis of a Diffusive SIR Model with Saturated Treatment in a Heterogeneous Environment

In this paper, we propose a diffusive SIR model with general incidence rate, saturated treatment rate and spatially heterogeneous diffusion coefficients. We first prove the global existence of…

Spatial dynamics and optimization method for a network propagation model in a shifting environment

In this paper, a reaction-diffusion \begin{document}$ ISCT $\end{document} rumor propagation model with general incidence rate is proposed in a spatially heterogeneous environment. We first summarize…

Global dynamics in a reaction–diffusion multi-group SIR epidemic model with nonlinear incidence

References

SHOWING 1-10 OF 25 REFERENCES

Spherical harmonics and integration in superspace

In this paper, the classical theory of spherical harmonics in is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic…

Berezin integration on non-compact supermanifolds

A geometric approach to scalar field theories on the supersphere

Following a strictly geometric approach we construct globally supersymmetric scalar field theories on the supersphere, defined as the quotient space S2∣2=UOSp(1∣2)∕U(1). We analyze the superspace…

Spherical harmonics and integration in superspace: II

The study of spherical harmonics in superspace, introduced in (De Bie and Sommen 2007 J. Phys. A: Math. Theor. 40 7193) is further elaborated. A detailed description of spherical harmonics of degree…

Killing Vector Fields and Superharmonic Field Theories

The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high…

Introduction to the Theory of Supermanifolds

CONTENTSIntroduction Chapter I. Linear algebra in superspaces § 1. Linear superspaces § 2. Modules over superalgebras § 3. Matrix algebra § 4. Free modules § 5. Bilinear forms § 6. The supertrace §…

Berezin integration and dimensional reduction

A basic theorem of elementary Berezin integration, relating integrals of the invariant ~2 + ~0 to those of just the c-number part ~2 in 2 dimensions lower, is discussed. Examples of such "dimensional…

Orthosymplectically invariant functions in superspace

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and…

Existence and uniqueness of solutions to superdifferential equations

The geodesic flow on a Riemannian supermanifold