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PS-3 integral equations and projective structures on Riemann surfaces. , 192:4, 479–514 (2001) Andrei Bogatyrev INM RAS, ul. ru Analysis and Mathematical Physics Trends in Mathematics, 49–76 c 2009 Birkh¨ auser Verlag Basel/Switzerland Generalized Hamilton–Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups Ovidiu Calin, Der-Chen Chang and Irina Markina Abstract. We study geometrically invariant formulas for heat kernels of subelliptic diﬀerential operators on two step nilpotent Lie groups and for the Grusin operator in R2 .

1). For a known Φ(x), the eigenfunction u(t) may be recovered by the Sokhotskii-Plemelj formula: u(t) = (2πi)−1 [Φ(t + i0) − Φ(t − i0)] , t ∈ I. 1. 4) δ = 2/(λ − 1), with H¨ older boundary values Φ(x ± i0). 2. The Riemann monodromy problem The lifting R3−1 (P(R3 )) of the pants associated to the integral equation consists of three components Os , s = 1, 2, 3. We number them in the following way (see Fig. 1): the segment [−1, 1] lies on the boundary of O1 ; the segment [c4 , c3 ] is on the boundary of O2 and the boundary of O3 comprises the segment [c2 , c1 ].

Funct. Anal. Appl. : PS-3 integral equations and projective structures on Riemann surfaces. , 192:4, 479–514 (2001) Andrei Bogatyrev INM RAS, ul. ru Analysis and Mathematical Physics Trends in Mathematics, 49–76 c 2009 Birkh¨ auser Verlag Basel/Switzerland Generalized Hamilton–Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups Ovidiu Calin, Der-Chen Chang and Irina Markina Abstract. We study geometrically invariant formulas for heat kernels of subelliptic diﬀerential operators on two step nilpotent Lie groups and for the Grusin operator in R2 .