In this talk, we point out that curvature-regular asymptotically flat solitons with negative mass are contained in the Myers-Perry family in five dimensions. These solitons do not have horizon, but instead a conical NUT singularity of quasi-regular nature surrounded by naked CTCs. We show that this quasi-regular singularity can be made regular for a set of discrete values of angular momentum by...

Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and torsion singularities, respectively, the method we propose provides a natural way of discretizing gravitational theories with torsion degrees of freedom like...

We prove that for the mean curvature flow of closed embedded hypersurfaces, intrinsic diameter stays uniformly bounded as approaches first singular time, provided all singularities are neck or conical type. In particular, assuming Ilmanen’s multiplicity one conjecture and no cylinder conjecture, we conclude in two-dimensional case always bounded. also obtain sharp $$L^{n-1}$$ bound curvature. T...

To study the problem of the assigned Gauss curvature with conical singularities on Riemanian manifolds, we consider the Liouville equation with a single Dirac measure on the two-dimensional sphere. By a stereographic projection, we reduce the problem to a Liouville equation on the euclidean plane. We prove new multiplicity results for bounded radial solutions, which improve on earlier results o...

The physical properties of the lamellar lipid-bilayer component of biological membranes are controlled by a host of thermodynamic forces leading to overall tensionless bilayers with a conspicuous lateral pressure profile and build-in curvature-stress instabilities that may be released locally or globally in terms of morphological changes. In particular, the average molecular shape and the prope...

This article constructs a surface whose Neumann-Poincar\'e (NP) integral operator has infinitely many eigenvalues embedded in its essential spectrum. The is sphere perturbed by smoothly attaching conical singularity, which imparts Rotational symmetry allows decomposition of the into Fourier components. Eigenvalues components are constructed so that they lie within spectrum other and thus full N...

Vertebrate vision requires photon absorption by photoreceptor outer segments (OSs), structurally elaborate membranous organelles derived from non-motile sensory cilia. The structure and function of OSs depends on a precise stacking of hundreds of membranous disks. Each disk is fully (as in rods) or partially (as in cones) bounded by a rim, at which the membrane is distorted into an energeticall...