What are other peoples minds according to the Laṅkāvatāra Sūtra?

I read that everything is just my own mind from the Laṅkāvatāra Sūtra. If everything is my own mind, what about other peoples minds? Are they also my own mind? How can this be understood? For instance in Chapter 7 of the Laṅkāvatāra Sūtra there is this passage: > The Blessed One replied: There are four things by the fulfilling of > which an earnest disciple may gain self-realization of Noble Wisdom > and become and Bodhisattva-Mahasattva: **First, he must have a clear > understanding that all things are only manifestations of the mind > itself;** second, he must discard the notion of birth, abiding and > disappearance; third, he must clearly understand the ego-less-ness of > both things and persons; and fourth, he must have a true conception of > what constitutes self-realization of Noble Wisdom, provided with these > four understandings, earnest disciples may become Bodhisattvas and > attain Transcendental Intelligence. If all things are manifestations of my own mind, doesn't this mean Buddhism as expressed in this Sutra is the equivalent of solipsism? How do we understand the problem of other minds given this Sutra?