Heat Kernel Estimate in a Conical Singular Space
نویسندگان
چکیده
Let (X, g) be a product cone with the metric $$g=dr^2+r^2h$$ , where $$X=C(Y)=(0,\infty )_r\times Y$$ and cross section Y is $$(n-1)$$ -dimensional closed Riemannian manifold (Y, h). We study upper boundedness of heat kernel associated operator $${\mathcal {L}}_V=-\Delta _g+V_0 r^{-2}$$ $$-\Delta _g$$ positive Friedrichs extension Laplacian on X $$V=V_0(y) $$V_0\in {\mathcal {C}}^\infty (Y)$$ real function such that _h+V_0+(n-2)^2/4$$ strictly $$L^2(Y)$$ . The new ingredient proof Hadamard parametrix finite propagation speed wave Y.
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2023
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-023-01348-0