A note on parabolic convexity and heat conduction
Annales de l'I.H.P. Probabilités et statistiques, Volume 32 (1996) no. 3, p. 387-393
@article{AIHPB_1996__32_3_387_0,
     author = {Borell, Christer},
     title = {A note on parabolic convexity and heat conduction},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {32},
     number = {3},
     year = {1996},
     pages = {387-393},
     zbl = {0854.60058},
     mrnumber = {1387396},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1996__32_3_387_0}
}
Borell, Christer. A note on parabolic convexity and heat conduction. Annales de l'I.H.P. Probabilités et statistiques, Volume 32 (1996) no. 3, pp. 387-393. http://www.numdam.org/item/AIHPB_1996__32_3_387_0/

[1] H. Bauer, Heat balls and Fulks measures. Ann. Acad. Sci. Fennicae Ser. A. I. Math., Vol. 10, 1985, pp. 67-82. | MR 802468 | Zbl 0592.35057

[2] C. Borell, Undersökning av paraboliska mått. Preprint series No. 16, Aarhus Univ. 1974/75. | MR 388475

[3] C. Borell, Geometric properties of some familiar diffusions in Rn. Ann. Probability, Vol. 21, 1993, pp. 482-489. | MR 1207234 | Zbl 0776.35024

[4] C. Borell, Greenian potentials and concavity. Math. Ann., 1985, pp. 155-160 . | MR 794098 | Zbl 0584.31003

[5] H.J. Brascamp and E.H. Lieb, In Functional integration and its applications, edited by A. M. Arthurs, Clarendon Press, Oxford 1975. | MR 465645

[6] H.J. Brascamp and E.H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. J. Funct. Anal., Vol. 22, 1976, pp. 366-389. | MR 450480 | Zbl 0334.26009

[7] J.L. Doob, Classical potential theory and its probabilistic counterpart, Springer-Verlag, New York, 1984. | MR 731258 | Zbl 0549.31001

[8] A. Ehrhard, Symétrisation dans l'espace de Gauss. Math. Scand., Vol. 53, 1983, pp. 281-301. | MR 745081 | Zbl 0542.60003

[9] R.M. Gabriel, A result concerning convex level surfaces of 3-dimensional harmonic functions. J. London Math. Soc., Vol. 32, 1957, pp. 286-294. | MR 90662 | Zbl 0087.09702

[10] L. Hörmander, Notions of convexity, Birkhäuser, Boston, 1994. | MR 1301332 | Zbl 0835.32001

[11] B. Kawohl, When are superharmonic functions concave? Applications to the St. Venant torsion problem and to the fundamental mode of the clamped membrane. Z. Angew. Math. Mech., Vol. 64, 1984, pp. 364-366. | MR 754534 | Zbl 0581.73006

[12] N.A. Watson, Green functions, potentials, and the Dirichlet problem for the heat equation. Proc. London Math. Soc., Vol. 33, 1976, pp. 251-298. | MR 425145 | Zbl 0336.35046

[13] N.A. Watson, Mean values of subtemperatures over level surfaces of Green functions. Ark. Mat., Vol. 30, 1992, pp. 165-185. | MR 1171101 | Zbl 0784.35039