In the previous letter, arXiv:2210.16738[hep-th], we found a set of flavor mass relations as constraints that $\beta$-deformed $A_{n-1}$ quiver matrix model restores maximal symmetry in massive scaling limit and reported existence Argyres-Douglas critical hypersurface. this derive concrete conditions on moduli parameters which maximally degenerates Seiberg-Witten curve while maintaining relatio...

The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology. 1 Branching MWI space-times Two basic types of branching universe have been suggested in modern mathematical physics: universes which branch in a style befitting the ‘many-worlds...

Four constructions of constant mean curvature (CMC) hypersurfaces in S are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all values of the mean curvature. Second, ...

Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

We define the Segre numbers of an ideal as a generalization of the multiplicity of an ideal of finite colength. We prove generalizations of various theorems involving the multiplicity of an ideal such as a principle of specialization of integral dependence, the Rees-Böger theorem, and the formula for the multiplicity of the product of two ideals. These results are applied to the study of variou...