"We continue to hold Julian in our hearts with bright memories of him as a wonderful father, husband, explorer, lover of the natural world and the arts, and as an original and collaborative performer," the statement said.
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Sands, the 65-year-old British-born actor best known for his role in the 1985 film "A Room With a View," has been married for more than three decades to journalist Evgenia Citkowitz, and has three adult children.
They said they were "deeply grateful to the search teams and coordinators who have worked tirelessly to find Julian."
A June 17 search for Sands, the eighth organized search since his disappearance, was unsuccessful, authorities said. But the San Bernardino County Sheriff's Department said the case remains active.
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Sands, a longtime avid hiker and mountaineer, was reported missing January 13 after setting out to hike on the massive mountain, which was pounded by severe storms during winter.
Authorities said that while warmer weather made the latest search possible, parts of the mountain remain inaccessible due to dangerous conditions.
The Associated Press contributed to this report.