We consider the question of existence and non-existence of positive entire solutions for conformally invariant equations involving polyharmonic operator. We obtain existence of infinitely many positive solutions if the potential decays sufficiently fast at infinity and the nonexistence of positive solutions if the potential grows too fast at infinity. We also establish a Kazdan-Warner type cond...

On conformal manifolds of even dimension n ≥ 4 we construct a family of new conformally invariant differential complexes, each containing one coboundary operator of order greater than 1. Each bundle in each of these complexes appears either in the de Rham complex or in its dual (which is a different complex in the non-orientable case). Each of the new complexes is elliptic in case the conformal...

Granulomatous lobular mastitis (GLM) is a rare and benign condition of unknown etiology, which has been described recently. It primary affects young parous women and usually presents with a unilateral and extra-areolar breast mass. The condition may clinically mimic breast cancer, sometimes leading to misdiagnosis resulting in unnecessary breast surgery.We report two ca...