We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator of compact(with or without boundary) spacelike hypersurfaces of Lorentian manifold satisfying certain conditions,just in terms of the mean c...We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator of compact(with or without boundary) spacelike hypersurfaces of Lorentian manifold satisfying certain conditions,just in terms of the mean curvature and the scalar curvature and the spinor energy-momentum tensor. In the limiting case,the spacelike hypersurface is either maximal and Einstein manifold with positive scalar curvature or Ricci-flat manifold with nonzero constant mean curvature.展开更多
We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dede...We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.展开更多
文摘We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator of compact(with or without boundary) spacelike hypersurfaces of Lorentian manifold satisfying certain conditions,just in terms of the mean curvature and the scalar curvature and the spinor energy-momentum tensor. In the limiting case,the spacelike hypersurface is either maximal and Einstein manifold with positive scalar curvature or Ricci-flat manifold with nonzero constant mean curvature.
文摘We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.
