Let $M$ be a Stein manifold with smooth, strictly pseudoconvex boundary, and $x$ a point on its boundary. Is there a holomorphic function $f$ on $M$, smooth on the boundary, with strict maximum of $|f|$ in $x$?

This question was treated for domains in ${\mathbb C}^n$, but I could not find any reference for bigger generality.

Update. The set of maxima is called "Shilov boundary". For domains in ${\mathbb C}^n$, Shilov boundary is the set of strictly pseudoconvex points on the boundary, as follows from the paper

Richard F. Basener, Peak Points, Barriers and Pseudoconvex Boundary Points, Proceedings of the American Mathematical Society Vol. 65, No. 1 (Jul., 1977), pp. 89-92. https://www.jstor.org/stable/2041997

Let $M$ be a Stein manifold with smooth, strictly pseudoconvex boundary, and $x$ a point on its boundary. Is there a holomorphic function $f$ on $M$, smooth on the boundary, with strict maximum of $|f|$ in $x$?

This question was treated for domains in ${\mathbb C}^n$, but I could not find any reference for bigger generality.

Update. The set of maxima is called "Shilov boundary". For domains in ${\mathbb C}^n$, Shilov boundary is the set of strictly pseudoconvex points on the boundary, as follows from the papers

Richard F. Basener, Peak Points, Barriers and Pseudoconvex Boundary Points, Proceedings of the American Mathematical Society Vol. 65, No. 1 (Jul., 1977), pp. 89-92. https://www.jstor.org/stable/2041997

M. Hakim and N. Sibony, Frontiere de Silov et spectre de A(D) pour des domaines faiblement pseudoconvexes, C. R. Acad. Sci. Paris 281, Serie A (1975), 959-962.

Let $M$ be a Stein manifold with smooth, strictly pseudoconvex boundary, and $x$ a point on its boundary. Is there a holomorphic function $f$ on $M$, smooth on the boundary, with strict maximum of $|f|$ in $x$?

This question was treated for domains in ${\mathbb C}^n$, but I could not find any reference for bigger generality.

Let $M$ be a Stein manifold with smooth, strictly pseudoconvex boundary, and $x$ a point on its boundary. Is there a holomorphic function $f$ on $M$, smooth on the boundary, with strict maximum of $|f|$ in $x$?

This question was treated for domains in ${\mathbb C}^n$, but I could not find any reference for bigger generality.

Update. The set of maxima is called "Shilov boundary". For domains in ${\mathbb C}^n$, Shilov boundary is the set of strictly pseudoconvex points on the boundary, as follows from the paper

Richard F. Basener, Peak Points, Barriers and Pseudoconvex Boundary Points, Proceedings of the American Mathematical Society Vol. 65, No. 1 (Jul., 1977), pp. 89-92. https://www.jstor.org/stable/2041997