#### m-Pluripotential theory on Riemannian spaces and tropical geometry

Yıl: 2021 Cilt: 50 Sayı: 5 Sayfa Aralığı: 1347 - 1357 Metin Dili: İngilizce

m-Pluripotential theory on Riemannian spaces and tropical geometry

Öz:
In this study we extend the concepts of $m$-pluripotential theory to the Riemannian superspace formalism. Since in this setting positive supercurrents and tropical varieties are closely related, we try to understand the relative capacity notion with respect to the intersection of tropical hypersurfaces. Moreover, we generalize the classical quasicontinuity result of Cartan to $m$-subharmonic functions of Riemannian spaces and lastly we introduce the indicators of $m$-subharmonic functions and give a geometric characterization of their Newton numbers.
Anahtar Kelime: tropical varieties supercurrents m-pluripotential theory superforms

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
• [1] B. Abdullaev and A. Sadullaev, Potential theory in the class of m-subharmonic functions, Proceedings of the Steklov Institute of Mathematics, 279, 155–180, 2012.
• [2] E. Bedford and B.A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1-2), 1–40, 1982.
• [3] B. Berndtsson, Superforms, supercurrents, minimal manifolds and Riemannian geometry, Arnold Math. J. 5 (4), 501-532, 2019.
• [4] Z. Blocki, Weak solutions to the complex Hessian equation, Annales de l’Institut Fourier, 55 (5), 1735–1756, 2005.
• [5] A. Colesanti and D. Hug, Steiner type formulae and weighted measures of singularities for semi-convex functions, Trans. Amer. Math. Soc. 352 (7), 3239-3263, 2000.
• [6] A. Colesanti and D. Hug, Hessian measures of convex functions and applications to area measures, J. London Math. Soc. 71-1 (2), 221-235, 2005.
• [7] A. Dhouib and F. Elkhadra, m-Potential theory associated to a positive closed current in the class of m-sh functions, Complex Var. Elliptic Equ. 61 (7), 875–901, 2016.
• [8] F. Elkhadra and K. Zahmoul, Lelong-Jensen Formula, Demailly-Lelong Numbers and Weighted Degree of Positive Currents, arXiv:1809.00992[math CV].
• [9] V. Guedj and A. Zeriahi, Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (4), 607–639, 2005.
• [10] A. Lagerberg, Supercurrents and tropical geometry, Math. Z. 270 (3-4), 1011–1050, 2012.
• [11] H. Lu, Équations Hessiennes complexes, Thèse de l’Unniversité Toulouse III (UT3 Paul Sabatier), 2012.
• [12] A. Rashkovskii, Indicators for plurisubharmonic functions of logarithmic growth, Indiana Univ. Math. J. 50 (3), 1433-1446, 2001.
 APA SAHİN S (2021). m-Pluripotential theory on Riemannian spaces and tropical geometry. , 1347 - 1357. 10.15672/hujms.717867 Chicago SAHİN Sibel m-Pluripotential theory on Riemannian spaces and tropical geometry. (2021): 1347 - 1357. 10.15672/hujms.717867 MLA SAHİN Sibel m-Pluripotential theory on Riemannian spaces and tropical geometry. , 2021, ss.1347 - 1357. 10.15672/hujms.717867 AMA SAHİN S m-Pluripotential theory on Riemannian spaces and tropical geometry. . 2021; 1347 - 1357. 10.15672/hujms.717867 Vancouver SAHİN S m-Pluripotential theory on Riemannian spaces and tropical geometry. . 2021; 1347 - 1357. 10.15672/hujms.717867 IEEE SAHİN S "m-Pluripotential theory on Riemannian spaces and tropical geometry." , ss.1347 - 1357, 2021. 10.15672/hujms.717867 ISNAD SAHİN, Sibel. "m-Pluripotential theory on Riemannian spaces and tropical geometry". (2021), 1347-1357. https://doi.org/10.15672/hujms.717867
 APA SAHİN S (2021). m-Pluripotential theory on Riemannian spaces and tropical geometry. Hacettepe Journal of Mathematics and Statistics, 50(5), 1347 - 1357. 10.15672/hujms.717867 Chicago SAHİN Sibel m-Pluripotential theory on Riemannian spaces and tropical geometry. Hacettepe Journal of Mathematics and Statistics 50, no.5 (2021): 1347 - 1357. 10.15672/hujms.717867 MLA SAHİN Sibel m-Pluripotential theory on Riemannian spaces and tropical geometry. Hacettepe Journal of Mathematics and Statistics, vol.50, no.5, 2021, ss.1347 - 1357. 10.15672/hujms.717867 AMA SAHİN S m-Pluripotential theory on Riemannian spaces and tropical geometry. Hacettepe Journal of Mathematics and Statistics. 2021; 50(5): 1347 - 1357. 10.15672/hujms.717867 Vancouver SAHİN S m-Pluripotential theory on Riemannian spaces and tropical geometry. Hacettepe Journal of Mathematics and Statistics. 2021; 50(5): 1347 - 1357. 10.15672/hujms.717867 IEEE SAHİN S "m-Pluripotential theory on Riemannian spaces and tropical geometry." Hacettepe Journal of Mathematics and Statistics, 50, ss.1347 - 1357, 2021. 10.15672/hujms.717867 ISNAD SAHİN, Sibel. "m-Pluripotential theory on Riemannian spaces and tropical geometry". Hacettepe Journal of Mathematics and Statistics 50/5 (2021), 1347-1357. https://doi.org/10.15672/hujms.717867