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math.DG2026
Uniqueness for the Kähler-Yang-Mills equations
Vamsi Pritham Pingali, Chengjian Yao
A formula for the -K-energy functional for the Kähler-Yang-Mills (KYM) equations is provided in this paper. Using this formula and Chen's -geodesic equation on the space of K…
math.DG2026
The top Yau--Yang conjecture for Kähler manifolds with positive sectional curvature
Ved V. Datar, Vamsi P. Pingali, Harish Seshadri
We prove that the top wedge power of the Ricci form of a complete non-compact Kähler manifold with positive sectional curvature has finite integral. Using a result of Chen-Zhu, an…
math.DG2026
Uniformisation of complete Kähler surfaces with positive sectional curvature
Ved Datar, Vamsi Pritham Pingali, Harish Seshadri
We prove that any complete non-compact Kähler surface with positive sectional curvature is biholomorphic to , establishing the two dimensional case of the weaker form…