Spatial Three-Mirror Off-Axis Freeform Optical System without Any Symmetry

Mirror symmetry without corrections

We give geometric explanations and proofs of various mirror symmetry conjectures for T-invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre transformation. We discuss mirror transformations of (i) moduli spaces of complex structures and complexified symplectic structures, Hp,q’s, Yukawa couplings; (ii) sl (2...

Mirror Symmetry without Corrections

Anomalous Mirror Symmetry Generated by Optical Illusion

This paper introduces a new concept of mirror symmetry, called “anomalous mirror symmetry”, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown.

Log Mirror Symmetry and Local Mirror Symmetry

We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of “affine lines” of each degree in P\B, where B is a smooth cubic. On the other hand, we consider coefficients of a certain expansion of a function obtained from the integrals of dx/x ∧ dy/y over 2chains whose boundaries lie on Bφ, where {Bφ} is a family of smooth cubics. Then, for small degrees, they coin...

Solutions without Any Symmetry for Semilinear Elliptic Problems

— We prove the existence of infinitely many solitary waves for the nonlinear KleinGordon or Schrödinger equation ∆u− u + u = 0, in R, which have finite energy and whose maximal group of symmetry reduces to the identity.