arXiv research

Energy methods solve Dirac-type equations in 2D Minkowski space.

Study on monopoles with singularities on 3-folds, proving Fredholmness and calculating $L^2$-indices.

The paper proves formulas and theorems for Dirac-Witten operators on manifolds with or without boundaries.

We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provid…

The paper proves a theorem for a twisted Dirac operator on specific manifolds.

The paper proves a theorem for a twisted Dirac operator on specific manifolds.

Study on monopoles with Dirac type singularities in 3D space.

Study of Dirac equation with non-local nonlinearity on spheres.

Paper constructs Morse-Floer homology for Dirac-geodesics.

Researchers compute a residue cocycle for Dirac-type operators using modified Getzler calculus.

Proves K-K-W type theorems for specific types of operators.

Study shows strict inequality for Dirac-type equation on spin manifolds, leading to existence results.

Method to find critical points in vector bundles with fermionic coupling.

Formula for index of Dirac-type operators on stratified spaces.

We use the spectra of Dirac type operators on the sphere $S^{n}$ to produce sharp $L^{2}$ inequalities on the sphere. These operators include the Dirac operator on $S^{n}$, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers o…

The paper proves new theorems for Dirac operators on even-dimensional manifolds with boundary.

Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.

Classifies local boundary conditions for Dirac-type operators on manifolds.

The paper proves a theorem for 5D spin manifolds with boundary using Dirac operator perturbations.

Let $P$ be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various $P$-related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the reso…

A new method of singular reduction is extended from Poisson to Dirac manifolds. Then it is shown that the Dirac structures on the strata of the quotient coincide with those of the only other known singular Dirac reduction method.

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature operators on 4-dimensional manifolds with (resp. without) boun…

The Kobayashi-Hitchin correspondence is established for mini-holomorphic bundles on certain 3-folds.

Develops a theorem for a 6D manifold with boundary.

Generalizes Kastler-Kalau-Walze theorem to even-dimensional manifolds.

Study perturbs Dirac operator on 4D manifolds, proving Kastler-Kalau-Walze theorems.

Constructs equivariant spectral flow for Dirac-type operators on manifolds.

Study on symplectic Dirac operators on foliations, estimating eigenvalues.

Study eigenvalues and nodal sets of twisted Dirac operators on surfaces.

Study on Palais-Smale sequences for conformal Dirac-Einstein problem, proving existence of solutions.

We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real nu…

Study relates Finsler structures to Clifford bundles for flat metrics.

The paper explores Hermitian Clifford analysis and its connection to representation theory.

The paper proves new theorems about specific types of operator perturbations.

In this paper, we prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with two-fo…

Eigenvalues of Dirac operators on boundaries are large mass limits.

Proves Kastler-Kalau-Walze theorem for spectral Einstein functional on low-dimensional manifolds.

Introduces Chern-Dirac bundles on non-Kähler Hermitian manifolds.

Defines spectral Einstein functionals for sub-Dirac operators on manifolds with boundary.

This paper extends Dabrowski-Sitarz-Zalecki theorems to manifolds with boundary.

We study the higher spin Dirac operators on 3-dimensional manifolds and show that there exist two Laplace type operators for each associated bundle. Furthermore, we give lower bound estimations for the first eigenvalues of these Laplace type operators.

Paper introduces new fractional Dirac operator and Q-curvature.

Study on Dirac operators on 6D manifolds with boundary.

Proves new theorems for manifolds with boundary.

Develops Poisson and Dirac manifolds of compact types with applications.

We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.

We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the spectrum of a certain first-order differential operator on B, which can be constru…

The paper introduces spectral Einstein functionals for Dirac operators on manifolds with boundary.