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Central Limit Theorem for Intersection Currents of Gaussian Holomorphic Sections
Bin Guo
https://arxiv.org/abs/2603.04588 https://arxiv.org/pdf/2603.04588

On the first eigenvalue of the area Jacobi operator for complex curves in K\"ahler surfaces
Zhenxiao Xie
https://arxiv.org/abs/2602.22744 https://arxiv.org/pdf/2602.22744 https://arxiv.org/html/2602.22744
arXiv:2602.22744v1 Announce Type: new
Abstract: In this paper, we investigate the first eigenvalue $\Lambda_1$ of the area Jacobi operator for complex curves in K\"ahler surfaces, establishing an extrinsic counterpart to the classical Lichnerowicz theorem for the Laplace-Beltrami operator. By analyzing the second variation of a conformally invariant Willmore-type functional, we derive the lower bound $\Lambda_1 \geq 2\,\mathfrak{Ric}$, where $\mathfrak{Ric}$ denotes the infimum of the ambient Ricci curvature. For K\"ahler-Einstein surfaces with positive Einstein constant $\mathfrak{c}>0$, this bound reduces to $\Lambda_1 \geq 2\mathfrak{c}$. We then explore the equality case, computing the exact dimension of the corresponding first eigenspace in terms of the area, genus, and the dimension of a space of holomorphic sections. This analysis shows that the equality is achieved for all curves of genus $g \leq 1$.
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Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Symplectic foliated fillings of sphere cotangent bundles
Francisco Presas, Sushmita Venugopalan
https://arxiv.org/abs/1809.10363
- Instability of Legendrian knottedness, and non-regular Lagrangian concordances of knots
Georgios Dimitroglou Rizell, Roman Golovko
https://arxiv.org/abs/2409.00290 https://mastoxiv.page/@arXiv_mathSG_bot/113078258814855540
- Floer homotopy theory and degenerate Lagrangian intersections
Kenneth Blakey
https://arxiv.org/abs/2410.11478 https://mastoxiv.page/@arXiv_mathSG_bot/113316098418952654
- Slices for reductive group actions in algebraic and holomorphic symplectic geometry
Peter Crooks, Rebecca Goldin, Yiannis Loizides
https://arxiv.org/abs/2512.02956 https://mastoxiv.page/@arXiv_mathSG_bot/115654549153065527
- On the symplectic geometry of branched hyperbolic surfaces in genus two
Gianluca Faraco, Arnaud Maret
https://arxiv.org/abs/2511.23323 https://mastoxiv.page/@arXiv_mathGT_bot/115643648617235810
- Open-Closed String Field Theory from Calabi-Yau Categories and its Applications to Enumerative Ge...
Jakob Ulmer
https://arxiv.org/abs/2603.18186 https://mastoxiv.page/@arXiv_mathQA_bot/116260383969858357
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