Title: Rigidity of proper holomorphic mappings between equidimensional bounded symmetric domains
Abstract:We prove that any proper holomorphic mapping between two equidimensional irreducible bounded symmetric domains with rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3....We prove that any proper holomorphic mapping between two equidimensional irreducible bounded symmetric domains with rank <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="greater-than-or-equal-to 2"> <mml:semantics> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\geq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a biholomorphism. The proof of the main result in this paper will be achieved by a differential-geometric study of a special class of complex geodesic curves on the bounded symmetric domains with respect to their Bergman metrics.Read More