Heat coefficients of surfaces with curved conical singularities
Year: 2025
Type: article
Abstract: Let ( M , g ) be a two-dimensional Riemannian manifold of finite diameter with a conical singularity. Under the assumption that the metric near the cone point C is rotationally invariant, but not necessarily flat, we give an explicit formula for the coefficient $$b_{1/2}(C)$$ b 1 / 2 ( C ) in the heat trace expansion $$\operatorname {tr}(\operatorname {exp}(-t\Delta _g))\sim _{t\searrow 0} (4\pi t)^{-1}\sum _{j=0}^\infty a_j(M) t^j+\sum _{j=0}^\infty b_{j/2}(C)t^{j/2}+\sum _{j=0}^\infty c_{j/2}(C) t^{j/2} \log t$$ tr ( exp ( - t Δ g ) ) ∼ t ↘ 0 ( 4 π t ) - 1 ∑ j = 0 ∞ a j ( M ) t j + ∑ j = 0 ∞ b j / 2 ( C ) t j / 2 + ∑ j = 0 ∞ c j / 2 ( C ) t j / 2 log t . In the case that the Gaussian curvature K of ( M , g ) satisfies $$|K(p)|\rightarrow \infty $$ | K ( p ) | → ∞ as $$p\rightarrow C$$ p → C , we show that $$b_{1/2}(C)$$ b
Author: Dorothee Schueth
Institution: Humboldt-Universität zu Berlin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7110153064